At the risk of making myself unpopular, I suggest you put yourself down as living in your current place, your wife down as living in Kings Lynn, and claim single person discount on both.
If your maths is right, that sounds like lot. I know nothing at all about the market for flats in Kings Lynn, but generally 5% is nearing a respectable rental yield (aka it’s what you’d get renting the place out) but maybe that’s the point. They really don’t want empty properties.
It's a small one bed flat, band A, lowest council tax, currently 1800 council tax will double to 3600. Would say flat is worth about £80k. Might be bit more but even at 100k that's 3.6%.
In what I think is a good example of why the entire system is fucked, my Band F (not that big) house in London costs 1700 per year in council tax. Probably wotth c900k max. So about 0.2%!
It would. But my wife is attached to it and points out I spend a load on going to sporting events that she has no interest in, the flat is her thing to spend on.