BBC Local TV

Didn't Sky try out a local news service - Sky Tyne and Wear, IIRC. Unfortunately they didn't expand it beyond that trial.

Wasn't the BBC trial based in Hull, something to do with Kingston Communications?

Indeed. https://www.chroniclelive.co.uk/news/north-east-news/sky-tyne-wear-sky-closes-6387352

There was also ITV Local for a while.