[nvm0n2]

The UK uses FPTP and has at least three major parties in Parliament (Lab, Con, SNP) and in the past Lib Dems were big enough to enter into coalition. There are also smaller parties in the Parliament too, like the Greens and sometimes independent candidates.

The reason the US only has two parties is because those parties are sufficiently loose and internally democratic enough that there's no need to start a third party, when you can come in as an outsider and take over one of the existing ones. Parties in the UK exercise much tighter control over who can lead them, and so there's more pressure to set up alternatives. If the US big tent parties worked the same way you'd have more than two parties as well.