As she handed the group custodial sentences, the judge told the court that the demonstrators "wanted to be martyrs for their cause".
The protest group began a wave of protests in September, blocking the M25, other roads in London including around Parliament, roads in Birmingham and Manchester, and around the Port of Dover in Kent.
On Wednesday, nine protesters were jailed at the High Court in London after they admitted breaching the injunction by taking part in a blockade at junction 25 of the M25 on 8 October.
Ana Heyatawin, 58, and Louis McKechnie, 20, were jailed for three months, while Ben Buse, 36, Roman Paluch-Machnik, 28, Oliver Rock, 41, Emma Smart, 44, Tim Speers, 36, and James Thomas, 47, all received four-month sentences.
Ben Taylor, 37, was handed six months, after judge Dame Victoria Sharp ruled that his submission – saying that he would protest again if not jailed – was “inflammatory” and a “call to arms”.
She told Taylor the longer sentence was “to deter (him) from committing further breaches”.
The judge said: “The defendants, or some of them, seem to want to be martyrs for their cause and the media campaign surrounding this hearing appears designed to suggest this.
“We, however, have to act dispassionately and proportionately.”
Activists have branded the sentences “clearly disproportionate”.
The group and its supporters chanted, “We are unstoppable, another world is possible” as they were led to the cells through the dock by security officers.
An Insulate Britain activist addressing the media said Ms Smart, one of the nine, had announced her intention to go on hunger strike.
Watch: Who are 'Insulate Britain'?
LBC journalist Rachael Venables, who was in court for the sentencing, said the group then stopped chanting when told to by the judge.
Insulate Britain says it intends to continue with the protests, which have sparked anger among motorists and others affected by the blockades, until the government agrees to insulate homes.
A statement from the nine activists jailed was read by an Insulate Britain supporter outside the Royal Courts of Justice after the ruling.
It read: “By imprisoning us, the government shows its cowardice. They would rather lock up pensioners than insulate their homes.”
The statement, that compared Insulate Britain to Martin Luther King and the suffragettes, warned the public that “no-one is coming to save you” and that “breaking the law” was needed.
It added: “You have a choice. To act, to come and join us help change the tide of history, or to be a bystander and be complicit in enabling genocide.”
Liberty director Gracie Bradley described today’s sentences as disproportionate, saying: “For years, injunctions have been used by the powerful to stifle dissent and restrict protest rights, while demonstrators have been demonised.
“The right to protest protects all of us and is the cornerstone of a healthy democracy.”
Human rights barrister Adam Wagner said the case was the first he knew of where non-violent protesters have been jailed for breaching this type of injunction, calling the decision a "huge moment".
The High Court has so far issued five injunctions to prevent protesters from blocking roads.
Those who breach the injunctions could be found in contempt of court and face a maximum penalty of two years in prison or an unlimited fine.
Myriam Stacey QC, representing the government, said further committal proceedings will be issued against other Insulate Britain protesters by the end of the week, relating to protests on 27 October.
So far, 161 people have been involved in the roadblock campaign and there have been more than 800 arrests.
Watch: Police arrest Insulate Britain protesters in Dartford