They haven't been accepted in shops for over 10 years now. Cheques still see some use elsewhere, but are slowly being replaced by cash, cards and bank transfers depending on the use case. The Wikipedia entry (https://en.wikipedia.org/wiki/Cheque#United_Kingdom) sums it up pretty well.
There had been plans to phase out the cheque in 2018, however the portion of the population that still uses cheque wield popular sympathy, so the plan was abandoned.
Now the official line is that cheque's will continue as long as people use them, but substantial investment will be made in making digital transfers the default. This has meant replacing the slow BACS and expensive CHAPS with Faster Payments, and cash with contactless.
So cheque is accepted almost nowhere, almost dead, but is being strung along until the boomers are gone. It would be fine if it wasn't such a PIA to handle.
Checks have the advantage that they teach everyone patience - whenever someone at the supermarket checkout is taking a solid 5 minutes writing a check for $13.92, and then the cashier takes another 5 minutes going through some complicated ritual accepting the check as payment.