I recently found a useful page on the Chartered Institute of Patent Agents’ website, especially if you’re looking for which firms employ patent attorneys in which part of the country.
They publish a register of UK patent attorneys (don’t think it includes all patent attorneys but it’s a good sample), which you can filter by region. I’m not sure you’d get very far just writing to one of them for advice (probably get a standard “sorry, can’t help” response) but it does give you an idea of who’s employing them, including those research organisations who have their own in-house patent group.
For example, searching on Greater Manchester, you find that in addition to Mewburn Ellis, Marks and Clerk etc, Fujifilm Imaging Colorants (based out at Blackley) also employ their own patent agents. Looking beyond Manchester, in Cheshire, Astra Zeneca and Thermo Fisher Scientific also employ their own patent agents. Lancashire yields Pilkington, and Merseyside has Unilever R&D. It may not be comprehensive, but might give you a few more options to chase up.