Sorry, gotta disagree about the letters.
As a postman I have seen this many times over the years, with people doing flits owing money and the new owners getting letters chasing it.
If you don't know the new address of the person(s) and you are still getting mail, then an official redirection is not in place. As such, don't worry about the legalities of opening them, because there is no alternative action you could take, and, being realistic, if they owe money and have just done a runner, do they deserve any consideration?
I think "legalities" is clouded area anyway in this case - as I said, if you have no legitimate alternative, then you have to protect yourself, and I have known of situations where (if they can get away with it) an old address is used again - it is best to be on top of what might be happening.
More to the point, reposting marked unknown or gone away does very little except delay things. They can stay in the system for weeks, and assuming they get back to the sender, are they going to believe a sticker on the envelope - I think not.
The advice I always give, and it seems to work, is open the mail, advise the sender that the person they want does not live there, saying when you moved in etc.
The debts are not yours or in any way enforceable because they were incurred at the address.
Whatever you do, while there are debts trying to be collected, there is always a possibility a baliff may call. Again, you have no need to worry, but it would be an idea to have handy any official correspondence (utility bills etc) to prove you are who you say you are.
As I said, I see this all the time - once people start taking positive steps rather than hoping it will just stop, then the quicker it will stop.