If parking and speeding fines are coming through regularly and often, they haven't registered the car at a new address and awaiting new log book. They're aware the car is incorrectly registered, doing whatever the hell they like and expecting it all to never catch up with them.
It's registered and maybe insured in somebodys name, companies will start digging around for more information when they want to take the driver (or registered keeper, if they doesn't provide the name of who was driving at the time of the offense) to court for non-payment of fines.
If you get court summons OP you'll need to check your credit score with those organisations who do it. It's possible your credit score will be affected by someone having CCJ's at your address, so you'd need to get that person removed as they're nothing to do with you and not registered as living at the address at the time of the CCJ's.
There'll definitely be CCJ's if there's a court summons (I don't know if it'll make a difference for you to write to the court about the person not living there) because if there's a court case and they don't show up, which they definitely won't since they won't have received the sumons if it came to your address, then the company will win by default.
I don't know what the procedure is for obtaining a new log book these days if you've lost it. As you've the name these fines are addressed to, you might be able to find out via the electoral register where they live. I've no idea whether you could apply for a new log book pretending to be them and giving their details. I don't expect that's legal, but neither is what they're doing!