Lots of rescues tend to put rabbits up for adoption after they have been neutered, mainly because you can't bank on the new owners actually getting the neutering done, and one accidental litter from your new rabbit could wipe out so much of the good work in rescuing/neutering etc.
The bonus of having a slightly older rabbit (4-6 months) from a rescue though is that it will be neutered already, and probably vaccinated too, post-neuter you will be able to determine its personality (that cute little babies could become a very stroppy adult, even after neutering!), it will have been health checked, and you could even get it a bonded partner from the rescue at the same time.
I wouldn't have thought you would have to travel too far out of London before you find a rescue - what about your local RSPCA? Or call your local vets to see if they know of any rescues local to you (some are small and don't advertise)
Good luck in your hunt!