Specifically, a parliament that comprises representatives of which a majority voted to hold the Brexit referendum, to honor the Brexit referendum, and were later voted into office on a promise to implement its results, just passed a law to require the prime minister of the UK not to implement the will of the people on the day on which British law already required that it be implemented.
It was not a question of legality. It was too many options and no-one, absolutely no-one, was willing to compromise so that any one group could hold a position that would command a majority vote in parliament. Simples!