Extinction Rebellion said nearly 80 people had blocked roads leading to two printworks, at Broxbourne in Hertfordshire, north east of London, and at Knowsley, near Liverpool. Hertfordshire police said they made 42 arrests and Merseyside police made 30.
The Murdoch-owned Newsprinters works also print the Daily Mail, the Daily Telegraph and the Financial Times. Campaigners said they had taken the action to highlight what they regard as the newspapers' failure to accurately report on climate change.
But the action was condemned by Johnson. "A free press is vital in holding the government and other powerful institutions to account on issues critical for the future of our country, including the fight against climate change," he said on Twitter.
"It is completely unacceptable to seek to limit the public's access to news in this way," he tweeted.
A Newsprinters spokeswoman said the disruption meant printing had to be transferred to other sites.
"We apologise sincerely to any readers of The Sun, The Times, the Daily Mail, the Daily Telegraph and the Financial Times who may be unable to buy their usual newspaper this morning due to late deliveries," the spokeswoman said.
"This attack on all of the free press impacted many workers going about their jobs ... This is a matter for the Police and the Home Office," she added.
The Sun pointed out that Saturday's edition carried a piece from veteran naturalist and broadcaster David Attenborough.
The blockade was part of more than a week of protests by Extinction Rebellion, which says an emergency response and mass move away from polluting industries and behaviours is needed to avert a looming climate cataclysm.
On Saturday it also protested in central London, including holding a "die-in" in front of Buckingham Palace, where demonstrators lay under white sheets to represent corpses.
By James Davey