We have the concept of a "walk in centre", but there aren't many, they are over-subscribed and they can't do much (for instance prescribe antibiotics). The typical experience there is to wait for 4+ hours to then be seen by a nurse and either sent home or sent to A&E. I am not being cynical here either!
A subtle way that government has cut services is to hand things like walk in centres to local councils to run but without increasing the funding for the councils. The councils then close them and take the political flak. The UK is not a good place to be sick and poor.