The two SAS officers, who have left active service, claim the police they trained had not been subjected to adequate psychological and physical tests to establish whether or not they were suitable to use firearms. The police officers were often “gung ho” and unfit.

The soldiers believe members of the Metropolitan police team that shot dead Jean Charles de Menezes, the innocent Brazilian, on the London Underground in July would have been among those they trained, although they are not certain.

The two men have detailed their concerns in a written statement to The Sunday Times. The Independent Police Complaints Commission (IPCC) is expected to study their claims as part of its investigation into how de Menezes, wrongly suspected of being a would-be suicide bomber, came to be shot by a team from the Met’s CO19 firearms unit.

Leaked documents from the IPCC showed that de Menezes was not behaving suspiciously, as had been claimed, but was restrained by an officer before 11 bullets were fired at him at close range. Three missed.

A spokesman for the IPCC said: “If there are concerns being expressed about the wider issues of selection and training, I’m sure our investigation team would look at the evidence and make recommendations.”

The two soldiers describe a number of alarming incidents during police training at the regiment’s base in Hereford. The trainers have no authority to fail police officers they believe are unsuited to the job.

One of the soldiers said: “When the tension starts to rise and the adrenaline is flowing, the ‘red mist’ seems to descend on armed police officers who become very trigger-happy. This has been shown time and again in training exercises.”

The second soldier said: “We thought that police firearms officers were far more concerned with their personal image, dressing in body armour and looking ‘gung ho’, rather than their professional capabilities. I’m not surprised at the number of mistakes over the years.

“There is no assessment of physical fitness, no psychological profiling, nothing. It’s a major problem.”

The statement also describes a police training exercise run by the SAS in which an armed terrorist group was threatening to kill a hostage. The police team were to rescue the hostage using minimum force.

“I was playing the leader of the armed group and instructed the other members of my group to surrender peacefully once the final assault was initiated. Therefore there was no need for the police to open fire.

“But as the police assault group entered the room they began firing at everything. No one had moved; we were all stood with our hands on our heads.

“The response would have resulted in the unnecessary deaths of all the make- believe terrorists and the hostage alike. So much for the rule of minimum force.”

The SAS officers claim they often found police firearms units to be small “cliques” with professional standards below those found in the military. “In the bar after exercises, the police would still be carrying their pistols and have MP5s (machine guns) slung over their shoulder so they could pose for photos. The first question they always asked was whether we had killed anyone.”

They added that many security firms operating in Iraq had a policy of not employing former police firearms officers.

Yesterday the Met defended its officers. Superintendent Phil Manns, head of CO19’s specialist firearms unit, said: “The selection and training criteria for our firearms officers is extremely rigorous. We recruit only the very best and most suitable available within the service. All of the officers within CO19 are regularly trained to the highest of standards.

“I am proud of the professionalism, skill and judgment displayed by my officers. We are called to support unarmed colleagues or respond to emergency calls from the public between 30 and 40 times a day. Incidents where officers feel it necessary to fire are thankfully rare. This alone refutes an allegation that these officers are not suitable for this role.

“The nature of the role done by a member of the SAS and a police officer who carries firearms is incredibly different and should not be compared.”

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