To the best of my knowledge, no UK banks now even
cash uncrossed cheques, yet alone issue them (e.g. as 'counter cheques'). Something in the back of my mind tells me that it's connected to anti-money laundering legislation but I've got no evidence to hand to support that view.
The solicitor might well be prepared to hand you cash if you can visit his/her office. (It would definitely be regarded as 'unusual' but I see no reason why it should be regarded as 'impossible').
However all High Street banks now offer 'basic' accounts, which almost anyone can open. There can be a few restrictions but they don't apply to all banks. (Most banks won't, for example, allow undischarged bankrupts to open a basic account but,even then, there are exceptions, with Barclays and Cooperative both accepting such account holders). Perhaps it's time to look for such an account?
https://www.moneyadviceservice.org.uk/en/articles/basic-bank-accounts