Parliament must review the police's so-called "shoot to kill" policy for suspected suicide bombers, the Liberal Democrats have said.
Police thought Mr Menezes was a suspect in the 21 July incidents
Lib Dem MP Nick Harvey said the first use of the policy had been a "disaster", when Jean Charles de Menezes was mistakenly shot dead.
An Independent Police Complaints Commission inquiry is under way. It is also probing leaks to the media.
Police have said the policy is needed to protect the public from bombers.
Mr Menezes, a 27-year-old Brazilian electrician, was shot in the head seven times on a train at Stockwell Tube station on 22 July.
Special armed police wrongly believed he was one of four men wanted over suspected attempted bombings on London's transport network the previous day.
The IPCC is investigating the shooting. On Friday, it announced it was also investigating leaks to the media about details of its inquiry.
Those details appeared to contradict some of the initial police claims in the wake of the shooting.
Mr Harvey, who sits on the House of Commons home affairs committee, says the policy should be subjected to parliamentary scrutiny.
"There may be some circumstances in which the only way to stop an outrage from happening is to kill somebody, but we haven't until now lived in a society where police can come along and shoot people dead," he said.
"If we are now in that situation then it's in the public interest that there is an open debate about ... the manner in which it is going to happen and who is going to take responsibility for it.
"The first occasion it's been used has been such a complete disaster that parliament and the home affairs select committee must look into this."
Jane Winter, director of British Irish Rights Watch, which monitored human rights issues during the Northern Ireland conflict, said the policy did not protect anyone and should be abandoned.
The IPCC has appealed for witnesses to the shooting
"It's not deterring anybody from acts of terrorism and it's bringing us down to the same level as the terrorists we want to oppose," she said.
But Bob Milton, who served for more than 30 years with the Met Police, said the policy was meant to help officers make a split-second decision on whether a suspect could be carrying concealed explosives.
"We hope it would be a deterrent, but it is a means of stopping somebody intent on mass murder," he told BBC Radio 4's Today programme.
He said the Met considered other methods of dealing with suspects, such as CS sprays and tasers, but they were judged ineffective.
"The effort needed to detonate a bomb is very, very small and even if you injured someone they could still do that."
And he defended the officers involved in the Stockwell shooting: "We must judge the police officers on what they knew prior to the event, not afterwards."