This wasn't just a problem after WW1 but all through the 19th and the first half of the 20th centuries across the developed world. The prevalence of coal burning, for transport, heat and power generation meant that it was essentially an unavoidable problem and it was only with the reduction in coal use after the Second World War and legislation, the Clean Air Act being the most famous piece, that it ended. For example Downing Street was originally yellow but this was only discovered in the 1960s during renovations, as it had been black from coal pollution since at least the mid 19th century. As for the people, Peaky Blinders takes place in a working class part of Birmingham, most people therefore work in relatively 'dirty' surroundings and jobs, think factory workers, railway workers and the like. It was simply too much work to keep buildings and streets clean and was never really attempted on a large scale because the effects of the coal dust became accepted and were considered unavoidable. I hope this helps, if you have any more questions on this please ask and I will do my very best to answer.