If there's a draft then air must be coming in from outside. Check and plug any gaps for example where the the tumble dryer hose meets the wall.
I blame the feckless old twat who did the conversion (of Irish descent I'm sure you'll be surprised to hear). Never turned up before 10am, always gone by 2pm, clocked off at mid-day every Friday and turned a 3 and a half week job (his words) into a 7 week one. He went completely missing for 3 days around St Patrick's Day. We only took him on because he was a friend of in-laws, but never again Gives honest Irish tradesmen like Sword a bad name
