Tyke, I have read that parts of Liverpool and other cities didn't get real indoor plumbing until the 70's or something. The lack of modern sanitation was one of the components of the Beveridge Report.
I guess there were some parts but I wouldn't think it was the norm. I live in a terrace house with an extention at the back which contains the bathroom. That's common among terraced houses in this area. I recently got all the documentation that the bank held on my house following the mortgage being paid up, must look through in more detail to see if it has details on when that was added on.
My parents moved to the house I was born and brought up in, in the mid-50's because it had an indoor toilet and hot running water.
We got central heating installed in about 1970 and were first house in street with it.
To the OP, I'd also recommend some TV programmes like Andrew Marr's Post-War History of Britain.
When you realise that Britain stil had rationing until the mid 1950's, that what was a time of prosperity in the US was a struggle here. DW didn't realise how things were here in the aftermath of the war.
Sorry, seem to have strayed a little off topic there!