The Prime Minister has taken the rare step of inviting interim Labour leader Harriet Harman to a meeting of the National Security Council to consider the threat posed by Isis.

Expected to take place on Tuesday, it will be the first time an opposition leader has attended the top-level discussions since 2013.

It comes as the Government tries to build a consensus behind extending the RAF’s bombing campaign to include strikes against Isis in Syria.

“The PM thought it was important to ensure the Leader of the Opposition was fully briefed on the current situation,” a Downing Street spokesman said. “The shadow Defence Secretary, Vernon Coaker will also attend.”

While RAF strikes are being carried out against Isis in Iraq, they are not currently targeting the group’s Syrian strongholds, unlike their US counterparts.

It is thought that David Cameron believes the group needs to be confronted in both countries, but MP’s in his own party have loudly voiced their opposition to this.

So he would be reluctant to ask for a parliamentary vote unless he can be assured of Labour’s support in order to gain a Commons majority.

Mr Coaker has indicated Labour would “carefully consider” any new proposals from the Government, in a reversal of the position taken by his party’s former leader Ed Miliband, who made it clear he would block strikes on Syria.

A party spokesman confirmed that had been invited to the meeting, which is the Government's main forum for collective discussion of the threats posed to the country's security.

It is attended by senior ministers, with military chiefs and the heads of the intelligence agencies also regular participants.

Ministers also faced criticism over the decision to warn against all but essential travel to Tunisia, where 30 Britons were among the 38 holidaymakers gunned down on a beach in Sousse.

Isis claimed responsibility for last month’s attack by Seifeddine Rezgui who was shot dead by police shortly after his killing spree.

The North African country claimed the UK was playing into terrorists' hands with the warning and there were also complaints from tourists forced to cut short their holidays.

Tracey Caburn, who was on holiday with her mum and sister, called it “a disgrace” when she arrived back to Manchester Airport after cutting their break short.

“We would've stayed there,” she said. “We didn't feel threatened at all. There were guards on the roof, the gates, the beach. We wanted to stay.”

But Downing Street has insisted that “substantial” work was needed in Tunisia to improve security for tourists.