I have a joint current account with my husband, and another current account in my name only.
Businesses can have two accounts at the same bank, so I don't see why an individual shouldn't be able to.
As already stated you can have as many current accounts as you want with the same bank but I find it far more convenient to use different banks.
I know immediately what card relates to the account I want to use (no squinting at tiny account numbers); I got £150 incentive simply for opening an account as a new customer; these days transfers between accounts at different banks are instant.
There is also the compensation limit to consider, too, if you have over £85,000