My view from a purely human perspective is that your father should be involved, it will be a huge adjustment for him and is perhaps best carefully prepared for.
Assuming he has capacity, which he may well have with early stage dementia, my understanding is the H&W LPA can’t be used, it’s only when capacity is lost that attorneys can make decisions and even then with as much involvement as possible. Financial matters are different, the LPA can be used, with the donors permission, while they have capacity. I could of course be wrong, but this is how it was explained to us.
In my experience a move to a Home involves both. LPA’s. Age U.K. or the Alzheimer’s Society could advise I think.
You are all trying to act from a place of love and care in your fathers best interests bytheway. Perhaps an honest chat via zoom or something similar between you all would be sensible to allow everyone to share information and express any worries they may have.