Distributing dole is one of a mayor's duties, now seen more as a quaint custom. In Penistone, Yorkshire, the dole given by the mayor doesn't consist of pennies as the name would suggest but of flour, given to children rather than 'the poor'. It's distributed not in church but on the steps of the town hall, the market-place.
Penistone is a market town with a bridge over the River Don, on the modern Trans-Pennine Way. As a Countryfile programme discovered, bridges are a huge expense and only worth maintaining for well-used routes. Towns with mayors are the ones on major droving/trade routes, and the accompanying customs of giving out pennies/sweets/bread or, more commonly, collecting pennies are embedded in the old network of tolls.