In reply to FrankBooth:
It may be a bit late now, but...
Best you can do is to book a ticket in a plane that is lightly booked. You can make a guess on that by the ticket prices and/or the flight time. Then just rock up to the plane and speak with the people at the front desk who will try to allocate you a seat with none else in the same row. If you ask for this before booking they'll try to make you pay for 3 seats.
You will need to have a letter from the hospital explaining in clear terms that you are medically fit to fly, and that will have to be passed to and authorised by the airlines medical honcho or whatever it's called, so you better be at check-in well in advance. You can also try to get this authorised in advance (in fact apparently you must) but good luck getting that sorted over the phone...
You'll have to be able to enter and exit the plane on your own steam walking/hobbling/skipping, and will also have to be able to have the leg 'down' in a normal sitting position for take-off and landing.
If you land in one the crappy London airports expect to be ferried to the airport doors by one of those golf buggies and then dumped there, so make pick up arrangements clear before you fly.
Good luck!