Old £1 coins cannot be exchanged any more but only deposited into bank accounts. They can also be sold to coin dealers or any member of the public who is willing to buy them from you. Fourex machines will buy old £1 coins for 92.6p each.

Old £5 notes can be exchanged at commercial banks or the Bank of England. Without an account, only HSBC, Natwest and Barclays will generally do it but some bank staff will bend the rules, or just not bother with non-customers when they are busy. Travelex is not meant to do it at all unless you are actually conducting a transaction, but during the transition period where two series of notes were circulating, most staff would not mind helping out.

Commercial banks can exchange whatever they like, it's only that the older the note, the less likely they will be able to ascertain its authenticity. If an old note has a higher numismatic than face value, some wily bank staff may swap it for their own money, or keep them for friendly banknote dealers.