The UK isn't a two party system though. It has at least 5 parties in play right now (Lab, Con, Reform, LibDem, SNP). Reform is only small but is currently polling higher than any other parties, so their number of MPs would go up a lot if an election was held today.

FPTP isn't sufficient to get a two party system. The US has such a system because it combines FPTP with open primaries. In the UK the right is trying to rebuild a new party from scratch, because the Conservative party has no working mechanisms that would allow it to have its direction changed by its members. Whereas in the US open primaries give members a great deal of control, and that kills the incentive to create new parties. The current Republican administration is run by a group of former Democrats who came into the GOP from the outside - this isn't possible in the UK system.