Considering that it as been going on for nine years and you haven't had a visit from an enforcement officer, then they don't seem all that concerned. I would think that this is more of a database error, which no one as bothered to correct.
A letter, telephone call, email or possible surgery consultation with your local MP might resolve the issue!.
I notice that the licencing authority have stated that their enforcement officers 'do not' have a right of entry into peoples property. I wonder how many of these enforcement officers have been naughty people, and insist that they inspect your property for possible misdemeanours!.
Everytime we buy a new TV I get letters from them. I have always ignored them because the licence is in my wifes name. Surely they must have it all stored on computer and if they can't be bothered to check I am not going to do it for them. We been hear 17yrs now and no one has ever called to check.
For your own peace of mind, your should write to them once aagin informing them that you have a licence but this time you need to explicity state that you are withdrawing their implied right of access. They must respond to this and accept that they may not force an entry to your property.