There are a number of reasons why clogs were popular in northern England in particular.
Firstly, the thick wooden soles of clogs helped to prevent the wet and cold seeping through, and insulated feet from the cold flagstone floors in the houses and mills. There was no central heating at this time, so keeping warm would have been a daily struggle.
Clogs were worn with hand or machine knitted socks. Knitting was a craft learnt by all members of a family, and a skilled knitter can work in quite low levels of light, making this a perfect evening family activity, where the lack of electricity and the cost of candles meant that low light levels were the norm in most Victorian workers houses.
There was also another practical reason why clogs were so popular, and that was safety. Workers in factories that processed hot and molten metals wore clogs to protect their feet, both from the impact of falling debris, and also because they were easy to shake off if bits of hot metal fell inside them. Safety clogs are still used in industry today, and are constructed to meet modern safety standard EN345. They are reported to be at least twice as strong as safety boots!
Clogs were incredibly strong and hard wearing, and relatively cheap. These made them an attractive option for working people, who needed reliable footwear at a price they could afford.