A Prime Minister might be considered to have more power than an American president because they control government’s legislative arm (the House of Commons). But that legislative body can also choose to eject the Prime Minister at any moment, whereas a President has four years of almost guaranteed power.
That would be a vote of non-confidence right? That can only happen when Parliament is sitting, and (AFAIU) the PM can prorogue Parliament at any time (with the rubber stamp of the Governor General). It looks like Parliament must sit once every 12 months, but I'm not clear if random motions can be presented during those sittings.