The high court has granted an interim injunction preventing protesters from occupying roads around Britain’s busiest port.

It comes after Kent police arrested 39 people when activists with Insulate Britain – an offshoot of climate change group Extinction Rebellion – sat down on roads in and out of the Port of Dover at about 8.20am on Friday.

The demonstration, part of an ongoing campaign to tackle fuel poverty and reduce the UK’s climate emissions, created long queues of vehicles, with several drivers remonstrating with the activists.

Transport secretary Grant Shapps said: “We are absolutely committed to protecting the right to peaceful protest, but it is unacceptable that people cannot go about their day-to-day businesses and that businesses or critical supplies should be put on a knife’s edge because of the reckless actions of a few protesters.”

Those who breach the injunction, granted to National Highways, will be in contempt of court and at risk of imprisonment and an unlimited fine, the government said.

The protest group – which is demanding that all UK housing is fully insulated by 2030 – have brought widespread disruption since its launch 10 days ago, with activists repeatedly blocking sections of the M25.

They have been condemned as selfish and dangerous by politicians and drawn an angry reaction from many motorists.

Earlier this week, the government successfully applied to the high court for an order that prohibits anyone from blocking the M25 – the scene of previous protests by the group. Anyone who breaks the injunction could be found to be in contempt of court, which carries a maximum penalty of two years in prison or an unlimited fine.

However, a spokesperson for the protesters said that injunction did not apply to the protests in Dover.

In a statement, the group added: “We are sorry for the disruption that we are causing. It seems to be the only way to keep the issue of insulation on the agenda and to draw attention to how poorly insulated homes are causing ill-health, misery and early death for many thousands of people.

“We are failing the country’s cold hungry families and the elderly and placing an enormous burden on the NHS.”

One lane of the A20 remained blocked on Friday afternoon with two protesters on top of a tanker, reportedly glued to the vehicle. One activist, who gave her name as Stephanie, said: “We do not want to be here. I want to be home with my family spending time with them, but if we don’t do this they aren’t going to have a future.”

Senior Conservative politicians have criticised the group, saying they are putting themselves and members of the public in danger. Shapps said: “Invading a motorway is reckless and puts lives at risk.”

The protesters have vowed to continue their campaign, which they say highlights the urgent need to improve the UK’s poor housing stock, rated as some of the worst in Europe, to tackle carbon emissions, fuel poverty and public health.

A spokesperson for the group said: “Insulating our leaky homes is one of the most cost-effective ways to reduce carbon emissions and it has all these additional benefits – reducing fuel poverty, creating jobs, reducing the burden on the NHS and protecting people from overheating during future heatwaves. It’s a no-brainer. Boris just needs to get on with the job.”

A government spokesperson said peaceful protest was “a cornerstone of our democracy” but criticised Friday’s action saying it had “put lives at risk”.

“The demonstrations we have seen over the last few weeks have wreaked havoc on our roads, disrupted thousands of people and put lives in danger and we are taking action to prevent these kinds of guerrilla tactics being used in the future,” they added.