MPs have voted to proscribe Palestine Action as a terrorist organisation despite concerns that the move could risk criminalising legitimate protest.

The draft order to amend the Terrorism Act 2000 and proscribe the group, laid by the home secretary, Yvette Cooper, passed the Commons on Wednesday by 385 votes to 26.

The order also bans two neo-Nazi groups, the Maniacs Murder Cult (MMC) and the Russia Imperial Movement (RIM).

Outlining the government’s case to MPs, the Home Office minister Dan Jarvis said: “By implementing this measure, we will remove Palestine Action’s veil of legitimacy, tackle its financial support and degrade its efforts to recruit and radicalise people into committing terrorist activity in its name.

“But we must be under no illusion. Palestine Action is not a legitimate protest group. People engaged in lawful protests don’t need weapons. People engaged in lawful protests do not throw smoke bombs and fire pyrotechnics around innocent members of the public. And people engaged in lawful protests do not cause millions of pounds of damage to national security infrastructure, including submarines and defensive equipment for Nato.

“Proscribing Palestine Action will not impinge on people’s right to protest. Those who wish to protest or express support for Palestine have always been able to and can continue to do so.”

But Jarvis faced a backlash from some MPs who described the move as a “draconian overreach” and likened the group to the Suffragettes.

It will become a criminal offence punishable by up to 14 years in prison for anyone to become a member of and support the direct action of Palestine Action.

The independent MP for Coventry South, Zarah Sultana, said the move “lumps a non-violent network of students, nurses, teachers, firefighters and peace campaigners – ordinary people, my constituents and yours – with neo-Nazi militias and mass-casualty cults”.

She said the group had thrown “red paint not fire on aircraft linked to surveillance flights over Gaza”. “Instead of prosecuting them for criminal damage, which is what normally is done, the home secretary is using the Terrorism Act to proscribe them as a terrorist group. This is an unprecedented and dangerous overreach of the state,” she said.

Some MPs and human rights organisations critical of the government’s position suggested that bundling Palestine Action with the white supremacist groups had put political pressure on MPs to back the measure.

Jarvis rejected claims that the government was rushing through the legislation and insisted “there is no political convenience” to the government’s plans.

“What we are seeking to do today is ensure the security of our country,” he told the Commons.

After the vote, a Palestine Action spokesperson said: “We are confident that this unlawful order will be overturned. As United Nations experts have made clear, spraying red paint and disrupting the British-based operations of Israel’s largest weapons firm, Elbit Systems, is not terrorism.

“The terrorism and war crimes are being committed by Israel against the Palestinian people – armed and enabled by this government.”

Four people were arrested, including “a man who blocked the gates of Downing Street with his mobility scooter”, at a protest in Westminster on Wednesday evening, the Metropolitan police said.

A spokesperson said: “Officers have made four arrests in the vicinity of the Palestine Action protest taking place in Westminster this evening.

“Public Order Act conditions had been imposed to prevent serious disruption, requiring anyone taking part in the protest to assemble on Richmond Terrace, off Whitehall.”

Palestine Action is seeking a legal challenge against the government’s move to proscribe it. A hearing is expected on Friday to decide whether the ban can be temporarily blocked, pending further proceedings to decide whether a legal challenge can be brought.

On Tuesday the lawyers group Network for Police Monitoring and the Haldane Society of Socialist Lawyers had warned the home secretary in two separate letters that proscribing Palestine Action would conflate protest and terrorism. The letters collectively were signed by hundreds of lawyers and by UN experts.

Several UN special rapporteurs said they had contacted the UK government to say that “acts of protest that damage property, but are not intended to kill or injure people, should not be treated as terrorism”.

The proscription order will go to the House of Lords and final approval is expected within days.

Yasmine Ahmed, the UK director of Human Rights Watch, said: “The use of counter-terrorism legislation to proscribe Palestine Action is a grave abuse of state power and a terrifying escalation in this government’s crusade to curtail protest rights. The idea that a non-violent protest group could be classed in the same category as Islamic State or al-Qaida is utterly preposterous and sets an incredibly dangerous precedent.

“Politicians should not be wielding the power of the state to protect corporate interests and silence legitimate non-violent protest.”