This happened to a friend of mine - it wasn't a scam, but it was someone trying to get round their crappy credit record which was at their own address.
They used to rent my friend's property, so they had an (old) lease agreement, which was what we think they were using to open new credit accounts at my friend's address, even though the place had been purchased by my friend.
The woman used to call for her post and give a long story about why it was still coming to the address, but she had told the companies about forwarding, blah blah.
My friend accepted it the first time, was sceptical in month two, and then had had enough, so opened the post - mainly credit card statements - phoned up each company and said that the person had moved away, so they needed to stop sending letters, and she didn't have a forwarding address. As it's a data protection issue, the companies updated their records and my friend didn't receive any more post.
When the woman called for her post, my friend just said she hadn't received anything, and so the woman's forwarding instruction must have been actioned (obvs, given that was her story, the woman couldn't then backtrack and say that she hadn't given a forwarding instruction), so that was the end of it.
But yes, definitely open the post, tell the companies who are sending it. Intercepting the post is illegal, but intercepting here means getting the post before it reaches its destination address (this is why a postman won't hand you your post if they pass you walking down the street), no one is going to prosecute a homeowner for opening post sent to that address.