Two homes have been raided by police in light of the attacks, one in Saxilby, Lincolnshire and one in Greenwich.
“One of the best ways of defeating terrorism is to go about our normal lives,” Prime Minister David Cameron said outside Downing Street on Thursday morning.
After the attack yesterday afternoon in Woolwich, south east London, which left a serving soldier dead, two men were shot and taken to hospital where they are being held under arrest. One is said to be in serious condition.
The two men are thought to be known to security services through various investigations in the last eight years.
The identity of the deceased soldier is yet to be made public.
There are 1,200 extra police officers on duty across the capital as a result of the terrorist act.