Our downstairs cloakroom toilet smells and I am unable to work out the problem. I have checked the outside drains and they are not blocked. So, the sewer smell is coming back into the house.

When the upstairs bathroom was refitted the originally builders had not connected the soil stack to the air vent in the roof. No wonder there was a smell when we moved in! As a temp measure I connected a one-way value that had to be above the highest applicance. When the bathroom was eventually re-fitted the plumber connected it to the roof vent. What exactly does the soil stack do and shold there be one for the downstairs cloackroom?

The downstairs toilet flushes OK. The u-bend comes out the back of the toilet and straight on to the sewage pipe in the floor and out the house. Could it be the wax washer/connector? Not sure I got that quite right.

Good chance that it is the wax ring that is bad, incorrectly installed in the first place or even missing. You will figure it out when you take the toilet off and replace it. If the original plumbers didn't connect the stack to the roof vent I wouldn't put anything past them. WHERE was the inspector? Without knowing more about your installation it sounds like the lower commode is vented through the stack that serves the 2nd floor. This is normal practice subject to lateral distance limitations. If it flushes OK and no other drains make noise during or after the flush things are probably vented OK.

I totally agree with ER , this was a slock job from the start so check everything starting with the wax ring. The vent stack allow some sewer gas to escape the system but its primary purpose is to allow air back inside the pipe to replace the water as it drains. Without proper venting you get drains that chug and gurgle and frequently stink to high Heaven.