We have fascists, communists, and anarchists in the UK, but I don’t think they have any interest in attacking Christians. That may be the difference.
We are often told by our Security Service that the greatest threat to our internal security is from the far right. However, I doubt that the Catholic Church is a serious target for them. We do have some Polish churches, and it’s very possible that they could be targets of far-right terrorism, but they would be targeted, as other premises have been, because they are Polish, not because they are Catholic. For the most part, the far right is concerned with attacking Muslims, Jews, ethnic minorities, and the LGBT community.
British communists are not generally violent. As illustrated, they are actually somewhat ridiculous. The real danger posed by the British far left is entryism. I am sure that they are not interested in attacking churches. They do tend to be rather anti-Semitic.
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I’m not sure exactly who counts as an anarchist, but there are certainly people with anarchist tendencies within groups such as Extinction Rebellion and Occupy. They are a nuisance. They damage property and they disrupt essential services. Occupy London did cause serious problems for St Paul’s Cathedral, but that was because they set up a camp outside the cathedral, simply because the cathedral is in the middle of the City of London. The protestors actually made it clear that their protest had nothing to do with the cathedral, apart from the fact that they happened to camping outside it.