In normal times, taking the Avanti train service from Edinburgh to Birmingham then an onwards connection to Southampton is a great option.
But...... For the last few months the Avanti service has been little short of a disaster. Endless cancellations, and the route from Edinburgh is especially badly hit. This is because the management have failed to manage recruitment and simply don't have enought crew to operate the schedule.
One would hope that by the time you travel, this crisis will be over and the service will be running smoothly again. But they've had months to fix things and there is precious little sign of improvement, so if you are thinking of doing this option then you need a keep a watching eye on this.
