If your mother has lost capacity you can only perform limited actions under the LPA unless it is registered. That is why I asked the question.
Theoretically, under the Mental Capacity Act, as an attorney you can act with all the powers of a beneficial owner. However, the difficulty you have is that if your mother dies and you are not the sole residuary beneficiary of the estate, the residuary beneficiaries will want the house sold. If you are the sole residuary beneficiary (and it includes the house - ie the house is not specifically bequeathed), I do not foresee any problems, other than the fact that if she has to make a contribution to care home fees, the LA may seek the sale of the "new house".
This particular case is extremely fact sensitive. I really can't emphasise enough that you should take legal advice from an appropriately qualified lawyer.