I agree with Lankeela, the RSPCA would almost certainly kill it.
I would try other places first and to be honest I would rather leave it feral than contact the RSPCA.
Could it possibly have eyesight problems? It is strange for a cat to be dirty, plus you say that it knocks into things and gets under your feet. It may be worth a quick vet check if you decide to let it stay - there may be a simple solution to its problems (eg an ear infection that is easily cleared up with antibiotics).