HSBC will take most old notes (at least from Page onwards). Everything else, even in limp and dirty condition, sells for more than £1. However, this can only be guaranteed in proper city centre branches because some small branch managers are stupid.

HSBC and Lloyds also take old coins. Pre-decimal coins should be bagged in whole pounds. I am told that Natwest Islington takes everything, but have never needed to try as HSBC has always exchanged anything I needed to.