Globaliser

Normally, I would recommend that you change from the Piccadilly Line to the District Line at Barons Court. This is a cross-platform change that involves a walk of about 10 feet. However, you can also change from the Piccadilly Line to the District Line at Hammersmith (which is one stop before Barons Court). This is also a cross-platform change, but you may have to walk about 20 feet to get to the other side of the platform. In either case, you take the Piccadilly Line from Heathrow to the change point (ie Hammersmith or Barons Court), and you take the District Line from the change point to Westminster.

Directions here from a previous thread (the Park Plaza County Hall is pretty much directly across the street to the north of the Park Plaza Westminster Bridge): Bus, Train, Car to Tube from Heathrow Bus, Train, Car to Tube from Heathrow The Tube from Heathrow to Westminster should be just over 60 minutes, plus maybe 10 minutes to walk over the bridge to the hotel.

While we're on the topic of alternative routings, can I please suggest a couple of things that the OP (or anyone else with luggage) should try to avoid: Do not go by Tube to Waterloo on either the Bakerloo or Northern Lines - there is no step-free exit, so luggage will be a pain. (And the exit is less convenient for the Hampton, anyway, as Cotswold Eagle has said.) Do not change from the Piccadilly Line to the Jubilee Line at Green Park, because the signed route is painful (and the lifts are relatively unreliable, so you may have to carry luggage up/down stairs); and using the alternative "cheat" route really requires some experience of handling luggage on escalators, without which that can be very dangerous.

For the Hampton, I would actually change again at Westminster. Get on the Jubilee Line. It's only one stop to Waterloo, but if you then follow the way out signs from the Jubilee Line you'll get tipped out on to Waterloo Road. It's only a 300-yard walk from there to the Hampton. Changing at Westminster is step-free via lifts (elevators), and there is step-free exit from the Jubilee Line at Waterloo. For paying on the Tube, I think that the last thing that I would do - literally, in that it's the emergency measure of last resort - is to "buy a ticket". Use a contactless payment card (or buy a pre-pay Oyster, if that's in your plans). Touch in at the gate at the start of journey as you enter the station through the gate line, and touch out at the gate when you exit the station at the end of the journey, and you will be charged the correct fare. (You must do this even if the gates are open, otherwise you'll be charged a penalty fare.) If you use the same payment card all the time, you'll also benefit from daily and weekly (Monday to Sunday) capping, if you use London public transport enough to reach a cap. If you can pay with your payment card via your phone (Apple Pay or Google Pay), that works too. (Much to my constant annoyance, but that's another story.) Given where you're staying, a trip to Windsor should be dead easy. As should getting to Southampton by train. It'll probably be rather faster than doing it by road. The closest entrance for you to Waterloo mainline station for these trains is basically exactly where you get out of the Jubilee Line on to Waterloo Road.

For clarity: one station is called Windsor and Eton Riverside. This has trains to/from London Waterloo on a route via Clapham Junction, Richmond and Staines, operated by South Western Railway. the other station is called Windsor and Eton Central. This has trains to/from Slough, operated by Great Western Railway; that is only one station away so it is literally a shuttle service.

And there's actually more designated luggage space on the Piccadilly Line than on the Elizabeth Line, although it's dual-use space in that it can be used for standing when there's no luggage there. But the space is designated - and if you're starting your journey at Heathrow then you will almost certainly find both luggage space and a seat for yourself:

Which hotel? It does have a bearing on the merits of your proposed route from Heathrow.

No lockers, as far as I know. But the company that operates the left luggage service at railway stations does have a location at St Pancras. Details are available on https://www.excess-baggage.com/our-locations.php or https://www.left-baggage.co.uk/en/locations (they're the same company).

This is not true. In the UK, unions must give at least two weeks' notice of any strike. So even if you don't receive any notification, you can check for yourself two weeks before you travel.

Realistically, I don't think there's any way you'd be able to get that much time in London. You'll probably need to store your bags somewhere, which would take time; and then you'd also have to allow time to retrieve them before your train to Paris. At some stage, you'd need to transfer yourselves and your bags across town from Waterloo to St Pancras. And you do have to allow time for check-in (including security and immigration) at St Pancras before boarding your train; Eurostar's recommendation is to arrive at St Pancras 90 minutes before departure time, and ISTR that there were times recently when you really needed that much time. So lunch, yes, but probably very little more than that.

What time is your train to Paris?

sddsddean is right about this if you book those cheaper fares, which are Advance fares that are valid only on the booked train. If you want flexibility, you can also choose to pre-book a flexible ticket which (on that route) is at the Anytime (walk-up) fare of £52.00. You might choose to do so in order to avoid the hassle of buying a ticket after reaching the station. If you pre-book a flexible ticket, you will be asked to specify a train - but you do not have to travel on that train even though you have pre-booked, and you can travel on any train for which the ticket is valid (which on that route is, I think, every train).

You may think that it's "expensive", but actually you're probably paying a cheapie rate and not for a full-fare ticket. Those with status (which can be from any oneworld airline) also think it's much less ridiculous. History shows that those who don't have to pay for pre-allocation (which also includes full-fare passengers) can account for something like two-thirds or more of the passengers in the cabin. These are the more valuable customers whom the policy benefits.

If you're travelling on a through ticket, then any LHR departure time from 13:40 would be legal (although not necessarily advisable) - that is the official Minimum Connection Time for this connection. So you have a further 3½ hours on top of that, which should give you an indication of the generosity of margin that you have. You do not need to arrive at LHR three hours before your flight to Barcelona. If you are there 60 minutes before your onward flight, you will have enough time to drop your bag, clear security and get to the gate. A private inter-airport transfer is considerably more costly than necessary. National Express run a perfectly good inter-airport transfer service.

I remembered that Mrs f. had actually been kind enough to describe the Moxy at the time: Moxy Hotel Southampton Moxy Hotel Southampton Moxy Hotel Southampton

0 stops is very unlikely. On the current timetable, the fastest trains generally have 3 intermediate stops, and the other fast trains generally also stop at Clapham Junction. It actually looks like there aren't any slower trains in the current timetable, but IIRC there used to be a third train every hour that took about 15-20 minutes longer and called at more intermediate stops. It's actually more important to check that there are 0 changes. There's generally no reason to choose a journey that requires you to change between London Waterloo and Southampton Central. The exception is if there are engineering works or there is disruption for some other reason, in which case things will by definition be out of the ordinary anyway. But mickeysgal is absolutely right: before you book, you will be shown the journey time (or you will be able to work it out from the departure and arrival times). I think that for an occasional user there are few if any good reasons to use the Trainline to book, but that's already been covered earlier in this thread.

Your TA's advice is bad advice. Of the three main options, staying at an airport hotel for two nights (when you want to see some of London) is the least good. Commuting between the airport and a Bath Road hotel (because that's essentially what you'll be doing) will be either time-consuming and aggravating, or expensive, or both. This includes the day of your cruise, because if you use the NCL transfer from the airport to Southampton, you will probably have to go from your hotel back to the/a terminal at the airport. Why is it too late for you to change your plans? Also, is there a reason for your assumption that you'll arrive at T3? All other things being equal, there's as much chance of you arriving at T5 as at T3.

The home page for the hotel's own website - https://www.marriott.com/en-gb/hotels/souox-moxy-southampton/rooms/ - says: All rooms have a 42-inch LED TV with premium entertainment options and high quality sound system

Fast trains from London Waterloo to Southampton Central take roughly 1¼ hours.

That depends on what criteria make it "good" for you. Personally, if my body clock is running on East Coast time, I prefer the latest possible flight. From NYC, that can often be nearly midnight, so arriving in the UK just before noon = 7 am NYC time, and your body will have been demanding sleep throughout the flight so you have a decent chance of getting some. Trying to navigate an airport and an arrival city when your body and brain think it's 2 am (and you haven't slept) is a big contributor to these short East Coast overnights feeling like hell on earth. For me, that's a high priority criterion.

Here's a moving illustration, in time lapse, of activity at this time of the morning. The landing aircraft are probably about a minute apart from each other in real time.

I don't think that's enough time. A 6.30 am arrival is one of the worst times of the day to arrive at Heathrow if you need to clear immigration. (For context, the night curfew is basically lifted at 6.00 am. The first non-curfew flight will land at 6.02 am, and then for the next hour or so it's pretty much a constant and continuous stream of arriving aircraft, mostly long-hauls on widebodies; there are so many at this time of the day that it's one of the periods of the day when Heathrow will sometimes use both runways for landings at the same time.) Even if you can use the e-gates, there will very probably be queues for them which can take quite a few minutes to navigate. If you have checked bags, you'll also need to get to BA's check-in counter at Terminal 3 before that closes. I can't immediately remember whether that's 60 or 45 minutes before departure, but you would have to be physically present at the check-in counter before 7.25 am or 7.40 am or else the electronic shutter will come down and you'll have missed the flight.

Why are you going through immigration at all? Do you have two separate tickets? And which are your operating airlines? Which terminal(s) are your flights to/from?

And it's a Fuller's, which ISTR from previous discussions is a pub company that has a reputation for decent pub food.

The official interactive map does now show the Queen's Arms. Start here - https://maps.heathrow.com/?poiId=1701 - and zoom in on the south end of Level 5.