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 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 largest party decides who becomes prime minister (technically the monarch decides, but practically their choice is dictated by the largest party).