interest rate increase, but bank did not

If its not in the terms and conditions of the account you hold that the interest rate tracks the BoE rate, then there is no reason why it should.

Why do you believe that the BoE interest rate ahould directly affect interest rates paid by the commercial banks?

I'm shocked

You need to remember that your bank sets its own interest rates for the savings accounts it offers. Just because the BoE has increased rates it doesn't mean that your bank will follow suit. You might ask, 'So what is the point in the BoE doing anything when banks can seemingly do what they want anyway?' Good question - answers on a postcard please.

Banks will often adjust their rates after a BoE rate change but there will almost always be a time lag - presumably whilst they work out what is best for them and their profitability (as if they haven't already done that!). They will also usually increase their borrowing rates first just to increase their margin (albeit temporarily). I also get the feeling that some banks are waiting to see what the competition will do before making their own move.

Anyway, from what OP says, their bank has now put its savings rates up.