OK, if your new flat has CT included then you have no liability elsewhere, so there shouldn't be an issue with declaring that your house is still your main home (and the other flat is "temporary"). You'd only have one CT liability, so you should be able to keep your single person discount on it. At least, that's how I'd view it, but I didn't work in CT directly.

Basically, it should be up to you to decide which your main home is, but the council will ultimately make the decision. But if you have furniture in the house, all the utilities are still connected, and you return to the house every weekend, it'd be difficult for them to justify not agreeing that it's your main home, even if you don't spend the majority of your time in it.