The Metropolitan police had no legal basis to detain David Miranda under the Terrorism Act 2000, Tony Blair's former lord chancellor has claimed.

Lord Falconer of Thoroton, who helped introduce the bill in the House of Lords, said that the act makes clear that police can only detain someone to assess whether they are involved in the commission, preparation or instigation of terrorism.

Falconer told the Guardian: "I am very clear that this does not apply, either on its terms or in its spirit, to Mr Miranda."

The peer, who served as solicitor general from 1997-98 and as lord chancellor from 2003-07, was highly critical of the home secretary, Theresa May, who praised the police action at Heathrow on the grounds that the partner of the Guardian journalist Glenn Greenwald possessed sensitive documents which could help terrorists and "lead to a loss of lives". May also said that police had acted within the law.

Falconer said that the home secretary's statement "is putting it too widely".

Falconer cited in detail the Terrorism Act 2000, which was passed as the government moved to crack down on dissident Irish republican terrorists in the wake of the 1998 Good Friday agreement, to show that there was no legal basis for the detention of Miranda. He said that schedule 7 of the act allows police to detain someone even when they have no grounds for suspicion. But he added that police can only stop an individual to determine whether they are involved in commission, preparation or instigation of terrorism.

Falconer said: "What schedule 7 allows an examining officer to do is to question somebody in order to determine whether he is somebody who is preparing, instigating or commissioning terrorism. Plainly Mr Miranda is not such a person."

The second paragraph of schedule 7 of the act says: "An examining officer may question a person to whom this paragraph applies for the purpose of determining whether he appears to be a person falling within section 40(1)(b)." This refers to paragraph 40 earlier in the act which defines a terrorist at (b) as a person who "is or has been concerned in the commission, preparation or instigation of acts of terrorism".

Falconer said that the provision in schedule 7, which allows the police to stop an individual even if there are no grounds for suspicion, is not designed for the likes of Miranda. He said: "What that provision is intended to allow is random searches where you've got a group of people, maybe everybody who is coming in from Northern Ireland on that ferry, where what you are going to do is search people. But there the examining officer, although he does not have grounds for suspecting any individual, has a perfectly good basis for doing random searches. Or he might think it is sensible to examine every third person because it is relevant or this is a way of getting to the truth.

"But that section plainly doesn't apply here. What is happening is they are targeting Miranda because they believe that he may have information that has been obtained from [the US whistleblower Edward] Snowden. The reason that doesn't fall within schedule 7 is because: even assuming that they think there is material which has been obtained in breach of the Officials Secrets Act, the action of Miranda or anybody he is acting with could not be described as somebody concerned in the commission, preparation or instigation of acts of terrorism. You could not reasonably believe, if you were the state, that Miranda is commissioning or assisting somebody to commission terrorism, to prepare terrorism or to instigate terrorism."

Falconer conceded that the word "instigation" in the act could be open to interpretation. But, he said: "You could argue that publishing this material could drive the world into such a frenzy that terrorism takes place. But that is much too wide a definition of instigation. What the act has in mind is people who are encouraging others, specifically and directly, to commit acts of terrorism, which neither Miranda nor Greenwald are engaged in. So my view – and I am very clear about this – is that schedule 7 does not cover what happened subject to one thing: if the government has got reason to believe that Greenwald or Miranda were engaged in something I know nothing about then obviously it might cover it – but from what has been said the basis of the stopping was a connection with the Snowden activities."

Falconer was critical of May who, along with David Cameron, was given advance notice of the police decision to detain Miranda. The home secretary, who said that police had made their own decisions about Miranda independently of ministers, praised them on the grounds that they suspected Miranda had information useful to terrorists.

The former lord chancellor said: "That [Theresa May's statement] is putting it too widely. The reason that the examining officer may question the person is to determine whether he is a person who is, or has been, concerned in the commission, preparation or instigation of acts of terrorism. What they are doing is winkling it much too wide. They are forcing into the wording of 40(1)(b), which is referred to in schedule seven paragraph 2, much too wide words."

Miranda was stopped at Heathrow en route to Rio de Janeiro, where he lives with Greenwald, who has written a series of stories for the Guardian revealing mass surveillance programmes by the NSA. He was returning to their home from Berlin when he was stopped, allowing officials to take away his mobile phone, laptop, camera, memory sticks, DVDs and games consoles.

During his trip to Berlin, Miranda met Laura Poitras, the US film-maker who has been working with Greenwald and the Guardian. The Guardian paid for Miranda's flights. Miranda is not a Guardian employee but often assists Greenwald in his work.