Hi - we've done the return trip from the Evelina a few different ways. Used a black cab with the pram which seems to go pretty well. If you use the Gett Taxi app you can choose a fixed fare - usually costs about 18 pounds or so which is actually cheaper than some of the private cabs. We've also used a company called Exclusive airports (except they do other trips too!) if you know the time you need them. We used them to get there from East Dulwich and they're so easy to book online with a carseat. although I suppose you might as well use Dulwich Cars if you were going to go this route. Not sure if this was helpful at all! But hope all goes well for the hospital visit.