I don't know about London but If you have any tortoise sanctuaries near you ask them if they take them for holidays. The nearest one to me does but make sure he gets his own space and doesn't have to share in case of disease, injury etc. There may be a tortoise club/society who can help.
Or ask your local vet or RSPCA if they know of anyone.
It may be worth checking with a few local pet sitters to see if any of them are experienced with tortoises... or at least competent and willing to learn. It would probably be less disruptive for the tortoise to get daily at-home wellness checks. If the tortoise needs supervised time outside, that may not be any more complicated than walking a dog or turning a dog out for supervised time in a back garden.
Whatever you decide, start working on good, clear instructions for caring for your individual tortoise.