Theresa May faced a call to arm all police officers at Parliament and other targets, as she confirmed a review to beef up security following the terror attack.

PC Keith Palmer, who was stabbed to death in the shadow of Big Ben, was not carrying a firearm – as is the case with many officers stationed around the Parliamentary estate.

Two armed plain clothed officers quickly arrived at the scene, shooting dead his attacker just a few yards away, within a few seconds of the stabbing.

Delivering her statement, the Prime Minister emphasised to MPs that the security measures had worked, because the man had been quickly stopped.

“In terms of security here in Westminster, we should be clear first of all that an attacker attempted to break into Parliament and was shot dead within twenty yards of the gates,” Ms May said.

“If his intention was to gain access to this building, we should be clear that he did not succeed. The police heroically did their job.”

But Theresa Villiers, a former Northern Ireland secretary, suggested it was time for all police who patrol areas “known to be of interest to terrorists” to be armed.

“As we reflect on what happened, is it time to consider whether the police who guard sensitive sites known to be of interest to terrorists, like Parliament, or like airports, should routinely carry personal protection weapons, even when those officers are not part of the units formally tasked with armed response?” she asked.

In response, Ms May said the level of security had been “enhanced significantly” over her 20 years in Parliament.

“As to whether individual officers undertaking particular duties are routinely armed, that is an operational matter for the police themselves,” she added.

“They are the best able to judge the circumstances in which it is best for individuals to have those arms, but of course we have seen a significant increase in the number of armed response vehicles, the number of counter terrorism specialists, firearms officers.”

Earlier, the Prime Minister confirmed that the police, the Parliamentary authorities and the Cabinet Office were jointly reviewing security, but described that as “routine”.

Early today, extra concrete blocks were delivered to Parliament as the first visible sign of the extra security measures planned.

The review is certain to focus on the obvious weak spot of Carriage Gates, facing onto Parliament Square, through which the killer of PC Palmer entered.

The officers there are not armed, but instead present a friendly face to tourists, helping them to take photos of Big Ben. Armed officers sometimes stand behind them.

Because it is used by cars carrying ministers and staff with permits to park underneath New Palace Yard, the heavy gates are frequently wide open.