It follows criticism over the force’s handling of the probe into suspected drone operations and the suspension of flights which ruined the travel plans of more than 140,000 people in the run up to Christmas.
Lord Harris of Haringey, who sits on the Joint Committee on National Security Strategy, suggested the disruption of critical infrastructure could justify the involvement of Scotland Yard.
John Woodcock MP, a member of the Home Affairs Committee, said there was now a case for a “different police force” to investigate the serious security incident.
Paul Gait, 47, and Elaine Kirk, 54, on Monday criticised the force’s “appalling investigation” after they were mistakenly arrested and held for 36 hours.
Cabinet ministers are also believed to be angry with Sussex Police for “messing up” by making contradictory statements about drone activity at the airport.
Transport secretary Chris Grayling said police “have not handled their communication response well” after detective chief superintendent Jason Tingley said there was a possibility there never had been any drones at Gatwick.
“This whole sorry episode shows why we need a nationally agreed and understood robust procedure for dealing with incidents like this,” Mr Woodcock told The Daily Telegraph.
“The country has been caught on the hop. There may be a case for a different police force [to get involved].”
Lord Harris, a former Home Office representative to the Metropolitan Police Authority, told the newspaper: “Clearly if you treated it like a terrorist threat, the Metropolitan Police would have been leading the operation.
“The old days of calling in Scotland Yard for a crime the local force can’t solve have probably long passed, but yes you could have done that.
“However, the margins between somebody playing around at an airport ... And somebody trying to do serious harm is probably quite a fine one and difficult to determine.”
On Monday afternoon, police chiefs in Sussex appeared to backtrack from remarks made on Sunday, insisting drone activity had taken place at Gatwick.
Sussex Police deputy chief constable Jo Shiner said: “We can unequivocally state that there have been numerous illegal drone sightings at the airport over three days from 19 to 21 December.
“There were numerous reports clustered around 37 occasions where a drone or drones were seen and I am keen for those responsible to be brought to justice.
“The impact of this criminal and reckless behaviour has been enormous and we are determined to locate those responsible to bring them to justice.”
On Monday Mr Gait and Ms Kirk condemned the way officers had detained them and searched their home, which they said had left them feeling “deeply distressed” and “completely violated”.
“The way we were initially perceived was disgusting, although those that know us didn’t doubt us for a second,” said Mr Gait.
Mr Lidington was said to have pressed for the Home Office and the Ministry of Defence to update their rapid deployment protocols for signing off requests for military assistance.
In a statement released later on Monday, Mr Wallace said systems are now able to be deployed across the UK to combat the threat of drones.
New drone owners were warned about the dangers of flying the devices as soon as they unwrap them this Christmas.
Police and aviation authorities urged users to read up on strict rules about the remote-controlled gadgets. Those caught flouting height and airport restrictions face a maximum fine of £2,500 and up to five years’ imprisonment.
Sussex Police has been contacted for comment.
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