No. They can't force servers in other countries to comply with their laws.
On top of that, even if UK users are somehow forced to shut down their servers, there's nothing stopping them from moving to a server elsewhere out of the jurisdiction of that law (good luck preventing that with a geoblock). This is why and how decentralized media can resist authoritarian censorship and why, even with its lesser funding and warts, it will always be the superior choice for anyone trying to resist surveillance states.