This is mostly written so I can copy-and-paste it on to forums where people keep getting this basic information wrong.
If you've ever moved house, you'll know how annoying it is to receive mail for the previous occupants. When those letters have a big red BAILIFFS ARE COMING warning on them - it is especially distressing.
The relevant section of the law is:
A person commits an offence if, intending to act to a person’s detriment and without reasonable excuse, he opens a postal packet which he knows or reasonably suspects has been incorrectly delivered to him.
Postal Services Act 2000 - Offences in relation to Postal Services - 84 (3)
You've just received a credit card through the post for the last tenant.
If you open it intending to steal money - that would be an offence.
If you open it because you're nosey - that is not a reasonable excuse.
If you open it so that you can call the company and let them know that their customer has moved - that would not be to someone's detriment, and would be a reasonable excuse.
That's what I do - several years after moving in and we're still getting post for the previous lot! A quick phone call is enough to stop most offenders. Occasionally a financial firm will be a bit sniffy about me not being able to confirm the recipient's account details - but most are happy to be informed.
It would be sensible to securely dispose of any mail afterwards - or mark it "return to sender - not at this address". But, yes, you can open misaddressed mail if you want to let the sender know their mistake.
I am not a lawyer - this is not legal advice!