No. Although there is a petition system in the United Kingdom, where such a petition is already being made, it is not binding.
- Even when a petition reaches the required number of signatures, the petition committee of the parliament will only consider putting it up for debate in parliament.
- Being put up for debate means just that: the parliament will have a discussion about it, nothing more. It does not mean that any MP will consider turning it into a proper act to vote on.
- And even when someone decides to do that, the parliament will vote on it as usual and can decide to dismiss it.
By the way, demanding a new general election because people are unhappy with the prime minister does not make much sense, because the prime minister is not elected by the general public. The general public vote the members of the parliament and then the parliament decides who becomes prime minister (technically the monarch decides, but practically they always pick the one the parliament wants). So when the UK public wants a new prime minister, they should petition the parliament to ask the queen to appoint someone else. A reelection does not necessarily reach that goal because the new parliament could just pick the same prime minister again.