He needs to get flea treatment from the vet, although I think a few shops sell vet strength treatments - seen something like that in Boots - and he needs to treat the house, again with vet strength treatment.
Buying some cheap rubbish from poundland or even something made by Johnsons isn't going to get to the root of the problem as most over the counter flea treatments only treat the adult fleas.
Sounds like he has a major flea problem and needs help to get it sorted out. If he's old and unable to walk his own dog I doubt he's going to have to energy to thoroughly vacuum his whole house and thoroughly treat it.
Perhaps a call to the RSPCA might help. They're supposed to support people in these sort of situations if programmes about them on television are to be believed.
Again, I think you should inform the charity that you're walking his dog for.