There are probably some arcane Parliamentary mechanisms where some sort of no confidence vote might trigger that result, but we don't directly elect the leader of our government, who by convention is the leader of the dominant political party in the House of Commons[1], nor the various ministers of state who will have executive authority (who are appointed by the PM[2]). This is probably the most significant of the "arm's length" mechanisms I mentioned before.
This can lead to obvious abuses of the system like Gordon Brown becoming Prime Minister in the final years of the New Labour administration, even though the electorate were promised repeatedly and explicitly at the last general election before that happened that anyone voting for New Labour was voting for Tony Blair to serve a full third term and would not get Gordon Brown as PM.
In fact, that situation is a textbook example of why I think a power of recall is long overdue. Whatever your political views or your opinion of the individual politicians involved, the facts are clear, the people exercised their right to vote on the one chance they were given, and then they got something they had explicitly been told they wouldn't get and had no recourse.
[1] Slightly different things may happen in a coalition where no party has an outright majority, as we discovered recently, but the position is still determined by the make-up of Parliament rather than a direct vote by the general population.
[2] Technically speaking, a lot of this is probably up to Her Majesty, but I suspect any refusal by the monarch to follow convention in this respect would start the countdown to our becoming a republic, so I consider this a formality.
A vote of no confidence in the HoC is constitutionally a signal for the PM to resign, but it's just a custom (which some PMs, notably Pitt, have ignored).
The PM is appointed by the Sovereign, and actually doesn't need to be an MP. While there's doubt over whether a Sovereign would appoint someone who isn't, it would be constitionally simple to shuffle them off to a safe seat. So no, it's not simple to get rid of a bad PM at all.
Sorry, which information? If you mean which country am I in, the answer is England.