If you give somebody “power of attorney,” that doesn’t mean they suddenly become a lawyer.
It simply means they can legally sign papers and make decisions for you in the area in which you’ve given them that power.
In many, perhaps most, cases, lawyers are given power of attorney, but it doesn’t have to be that way.
The British have several additional terms for people who practise law.
Lawyer is a general term describing all of them. Solicitors do most of the office work, draft documents, talk to clients, and may only appear as advocates in the lower courts.
Barristers do most of the trial work, especially in the higher courts, where they are the only ones who may act as advocates.
Attorney has pretty much the same meaning in Britain as in America, one who acts on behalf of another.