If a mooselimb is already “known” to authorities - why are they allowed to stay in country??
If they are not a citizen, the government should be aggressive about deporting them if there is any concern. If they are somehow a naturalized citizen, the government should be aggressive about finding a way to revoke citizenship. If they are born here, then kick out all their relatives and associates who are not citizens and refuse to grant entry to other relatives of them.
I think you are on the right track but the real solution is to attack this like organized crime. The mosques are making money off of preaching hate. I don’t know what the laws in the U.K. are but here you could bring RICO charges against the leaders of mosques when they preach hate to their parishioners who then turn around and commit violence.
When this happens, all members of the mosque who aren’t citizens should be deported. Anyone who earned a salary or any money at all through the mosque should be arrested and have their assets seized. The physical structure of the mosque should be destroyed and the land should be turned in to a memorial site for the victims of the violence that was committed. This should happen after EVERY terrorist attack. After awhile either there won’t be an mosques left or they will quit preaching hate and violence. If you had this happen enough times, I will bet your best informants will be the people working at the mosques. They won’t want to lose their livelihood because of some radical knucklehead who has been hanging around their mosque.