As I understand it, the house money is not taxable, but the other money shouldn't be (interest on both would be, of course). Consider them two pots of money. It sounds like you've mixed the pots together?
If so, it's important to separate them. Create one account for the house money, another account for other money. As I understand it, if the pots of money are mixed, the UK government will say the untaxable money is the very last money transferred out of the account. It's a version of last hired, first fired -- first remitted, highest tax. I think that's how it works. I'm not a tax advisor!
You might want a third pot of money that all the interest that has arisen since you moved to the UK goes into, since that's all taxable.
In sum, you may want to split into 3 accounts -- 1) house money, 2) money you already paid taxes on, and 3) interest on 1 and 2.
Is that helpful at all?