Hi, thanks for the answers.
I applied for the visa yesterday and was told the processing time was "a few days". Much to my surprise it took about 10 minutes.

It took me longer to fill all the forms in than it did for them to approve the visa!
So that's that sorted. I understand we do have a reciprocal healthcare agreement. To be honest, I hardly ever go to the docs, I was just making sure I'd be OK if I got hit by a bus or bitten by a nasty spider! Haha.
Not sure about the renting thing, all being well I'll have somwhere to stay (friends of a friend) while I look for a place to rent. Would still like to know if anyone has a rough idea of timescale though.