The threat of a terrorist incident occurring in Britain is officially rated as severe. This means that an incident is likely somewhere some time and everyone should be vigilant and prepared. But we should not get the threat out of proportion. An accident in the home or from traffic remains a bigger threat to life and limb.
The most horrific terrorist incidents in Europe recently have been in France, Belgium and Turkey. The greatest threat has been from Islamic extremists with a jihadist ideology who have been recruited by the Islamic State group and who seek "martyrdom" through suicide attacks. The number of incidents has seemed to increase as the territory controlled by IS has come under increasing pressure. There has also been a "copycat" element due in part perhaps to the media attention given to the details of the various incidents.
The weapons of choice have been guns and explosives, but these are much less readily available in European countries than in the United States. Britain has some of the most stringent gun laws and being an island is better able to stop the import of firearms. But explosives can be made in home laboratories and instruction manuals can be downloaded from the internet.