In the tram days, Birmingham like many cities had its own electricity department, and its own generating stations like Hams Hall. Payment for power was just a paper transfer of cost from one department to another.
Nowadays, it's all centrally controlled and as for electric railways, the companies are charged for an 'estimated consumption' of power, as are councils charged for street lighting.
Unfortunately the promise of electricity 'so cheap it wouldn't be worth putting meters in homes' never came to pass, as the nuclear power stations weren't as cost-effective as was first thought.