The Prime Minister said there would be “heightened security” as events are held across the UK to mark Armed Forces Day, amid fears of a similar attack on home soil.
The UK’s terror threat level was raised to “severe” last August in response to conflicts in Iraq and Syria - one level below “critical” when an attack is believed to be “imminent”.
Mr Cameron said: “There’s no doubt we face a very severe threat in our country and we have done for many months and many years, but the level of the threat is identified independently of government and published in the proper way.”
He said the most important thing is to “carry on” thanking the armed forces for their work “knowing that in our country we face a severe terrorist threat”.
But he said if people worked together, were vigilant and backed the police, “we can combat this poisonous narrative of Islamist extremism that is radicalising too many young minds in our country”.
Domestic terror arrests increased by almost a third last year, as police and religious leaders try to halt the number of people joining Islamic extremists in Syria.
There were 289 arrests for terrorism-related offences during 2014, an increase of 30% compared with the previous year. This was driven mainly by an increase in arrests in the three months to the end of December, the Home Office said.
Of the nearly 300 arrested, 111 were charged with an offence. Of these, 86% were considered to be terror-related. This is an increase on the 56% which were considered terror-related in the previous year, suggesting police were more frequently able to find evidence to support the link to terrorism following an arrest, the Home Office said.
The number of 18 to 20-year-olds arrested for terrorism-related offences increased from 15 to 46 last year.
It comes against a backdrop of counter-terrorism work by British police to stem the flow of disaffected young Muslims joining Islamic State fighters in Syria and Iraq to wage war against the West.
An estimated 700 Britons are believed to have fled to join Islamic militants, including three sisters and their nine children who left their homes in Bradford earlier this month.