I'm guessing you're not close to Heathrow then? You could always stay at Heathrow the night before?
Alternatively P&O and Marella do flights from round the UK as part of their package into Barbados/other Caribbean destinations.
If you still can't do the above and have to do 2 flights, have you looked at cruises departing from the Caribbean, they are generally much cheaper e.g. those departing from Puerto Rico. So rather than getting the second flight into Miami, you could fly into PR. (Although it's generally smaller/older ships).