You have my deepest sympathies as unfortunately, I suspect this is one you won't win.
In a real world the authorities would check your home, and they can do this without entry using one of those detector van thingies, confirm you do not have a tv and leave you peacefully alone. Unfortunately, this is not a real world anymore and these totally ignorant morons will not stop until they have badgered you either to death, or made you buy a licence just to get rid of them, even although you do not need or wish one. They used to be called double glazing salesmen, now they are Government workers. They are incapable of understanding anything not on their printed piece of paper/computer screen and if they believe that everybody in the UK will want to watch the garbage they put on the tv, then you must have a licence. You may even be lucky enough to find one with just about enough inteligence to understand, and accept your situation, but that will only last until the next moron comes along and starts it all again. Now if you had been from an enthnic minority (or anything that is not British), or had some form of criminality to your past they might have left you alone, because you could have threatened to sue them, and you may even have received a wad of dosh. But unfortunately you belong to the now endangered species of intelligent humans of normal English background, therefore it is their beholden duty to have you corrected at all costs.
My advice?? Contact your MP, if you have one and he/she is not on some expenses paid trip somewhere, and ask them to contact the Licence people on your behalf.
Or, once you have been driven insane by their incessant demands, buy the bloddy licence just to get some peace. It could be the cheapest option.
Or, of course you could just try shooting them when they come through the front door and pretend you are American............? Much more fun.