The Liberal Democrats have voted overwhelmingly in favour of an emergency motion criticising the anti-terrorism powers used to detain David Miranda at Heathrow for nine hours last month.

On the final day of their annual conference, all but one delegate voted for the motion after the Home Office minister Jeremy Browne condemned schedule 7 to the Terrorism Act 2000 as "too broad and overbearing".

Sarah Ludford, the Lib Dem MEP who secured the debate, said she suspected the use of schedule 7 to detain Miranda "was no less than an attempt to intimidate and shut up the Guardian".

Miranda is the partner of the Guardian journalist Glenn Greenwald, who has written a series of stories about widespread electronic surveillance by the NSA, based on files leaked by the US whistleblower Edward Snowden.

Miranda had been carrying data from Laura Poitras, the filmmaker who has played a key role in reporting on the NSA files and is now based in Berlin, to Greenwald in Rio de Janeiro, before police in London seized his electronic equipment.

The Terrorism Act, introduced a year before 9/11 to crack down on dissident Irish republican terrorists, gives police the powers to detain an individual at a port or an airport even if they have no grounds for suspicion. Police then have to question the detainee to assess whether they are involved in the commission, preparation or instigation of terrorism.

In his speech on Wednesday, Browne said it was right that the police could stop and interview people at ports and airports. But he said the government would make substantial amendments to the act – drawn up before the detention of Miranda – to move the legislation "decisively in a liberal direction".

Browne said the changes include a reduction in the maximum period of detainment from nine hours to six, extending the right to consult privately with a solicitor, the extension of the right to have a person informed of their detention and the repeal of the power to take an intimate sample.

But the minister said of the unamended powers, which were used to detain Miranda: "We can all agree that previous schedule 7 powers were too broad and overbearing. They are an example of Labour's almost complete disregard for civil liberties. So it does jar for Liberal Democrats to hear Labour criticise us on the case of David Miranda or civil liberties more generally."

Ludford said she feared the act had been misused. "I find it difficult to be persuaded that this anti-terrorism power was appropriately used. It is the most draconian and uninhibited police power that exists in this country, brought in, as you would expect, by Labour.

"If Mr Miranda was carrying leaked material genuinely prejudicial to national security surely other powers – the Official Secrets Act springs to mind, or other statutes giving a defence of press freedom – should have been invoked.

"The suspicion arises that the use of heavy anti-terrorism powers was no less than an attempt to intimidate and shut up the Guardian."

Ludford said the experience of Miranda showed that the Lib Dems appeared to have wasted their time in blocking the so-called snooper's charter bill. "Julian Huppert and Nick Clegg and others expended a huge amount of energy last year to block the communications data bill … But the revelations in the Guardian – and let's hear it for Alan Rusbridger and his colleagues – suggest they wasted their breath."

Maajid Nawaz, a former member of the hardline Hizb ut-Tahrir group who is now executive director of the counter-extremist thinktank Quilliam, spoke out against the way Miranda was detained.

Nawaz, who was himself detained under schedule 7 after being imprisoned for five years in Egypt, said: "The issue is not Miranda and his use or misuse of this information … I don't support what Mr Miranda did, but I do support this motion.

"It is irrelevant as to whether somebody is deemed guilty or not to discuss the fact that they have a right to legal representation and they have a right to silence. If what Mr Miranda did is wrong, that is for the courts to decide.

"One thing we learned from reading Orwell is that security must never be used to debase us of our basic civil liberties."

David Goodall, the former Lib Dem crime and police commissioner candidate in Hampshire and the Isle of Wight, who said he had worked in the "national security and defence sector" for more than 30 years, was the only delegate to vote against the motion.

He told the conference: "In August this year the security services had good reason to believe that a person travelling through the UK had information that would aid and abet terrorist groups. This person was detained and was found to have thousands of documents of a classified nature. The information contained in these documents could help terrorist groups.

"It was the security services' belief that this person detained had links to someone whose aim was to publish these documents. If published, terrorist groups would have access to information that would enable them to avoid detection and so lead to terrorist attacks on this country. Therefore I believe it was correct that David Miranda was detained and that stolen documents were removed from his detention."

Goodall said the Guardian articles on the NSA files were the equivalent of publishing details about Bletchley Park in the Süddeutsche Zeitung during the second world war.

"I ask you to consider what would have happened 70 years ago in 1943 had a chap passed through Waterloo station with details about Bletchley Park and the police got a tip off that this chap aimed to publish the details in the Süddeutsche Zeitung.

"Would Churchill say, a: 'that's OK, let the chap get on the train and make sure he has a nice cup of tea'? Or would Churchill say, b: 'make sure the documents are taken off him and then let him get on the train'? Or would Churchill say, c: 'seize the documents, arrest the chap and detain him till the end of the war'?

"If you believe the answer to this question is a or b then I believe you will see a flock of flying pigs outside the hall at lunchtime."

Shami Chakrabarti, director of Liberty, said: "David Miranda's nine-hour detention exposed the scandal of schedule 7 and momentum continues to grow for overhaul of this breathtakingly broad power.

"The Lib Dem membership has now joined Liberty, more than 70,000 petition signatories and many others in demanding serious reform – the government should take note and repeal schedule 7 without delay."