Supposing a UK based exchange did manage to satisfy the banks and regulatory agencies that it was in compliance with all the relevant legislation, would anyone actually use it?

The Money Laundering / Terrorism / Payment Services regulations would seem to suggest that a compliant UK exchange would look something like this ...

Registration would involve:
- Sending a certified copy of Passport / Driving Licence (that is, a copy signed by e.g. an accountant / notary / bank manager).
- And a certified copy of a recent bank statement (not an online one!).
- Entering your address history for the last three years.
- Consenting to a credit check / electoral roll search.
- Waiting for a secret code to arrive by post and entering that to verify current address.

There would be no ability to send or receive bitcoins other than to/from a single bitcoin address you control. Changing that bitcoin address would probably require a lengthy process involving sending documents by post.

Deposits and withdrawals would involve paying a 1% fee to cover bank charges (faster payments aren't free for businesses). They would only be possible to/from your verified bank account (which must be in your name).