The organisers of this week’s Extinction Rebellion climate protests have vowed to step up the campaign by targeting Heathrow airport, as three people look set to spend a month in prison for their alleged part in protests.

The trio – Cathy Eastburn, 51, Mark Ovland, 35, and Luke Watson, 29 – were remanded in custody for a month following a protest in which activists climbed on top of a train at Canary Wharf station in east London to highlight the climate crisis.

The decision to deny them bail pending a trial in May came as Extinction Rebellion – the UK group behind the week-long protests – confirmed it would be targeting Heathrow airport at the start of the bank holiday weekend.

A spokesman for the group said: “We are approaching a moment in time when no one can say they did not know about climate breakdown. If David Attenborough is starting to tell the truth, politicians have no excuse to not act now.”

Activists block the road junction at Oxford Circus in central London on Thursday. Photograph: Tolga Akmen/AFP/Getty Images

Activists have successfully occupied four landmark sites across the capital since Monday morning in a bid to highlight the escalating climate crisis and demand urgent government action.

On Thursday night the Met police said they had arrested more than 500 people so far and had cancelled leave for some officers over Easter.

“This is putting a strain on the Met and we have now asked officers on the boroughs to work 12-hour shifts; we have cancelled rest days and our violent crime task force have had their leave cancelled,” the force said in a statement.

On Thursday as the demonstrations entered their fourth day, more people joined from across the UK. Others who had been arrested earlier rejoined the protests.

Q&A What is Extinction Rebellion? Show Extinction Rebellion is a protest group that uses non-violent civil disobedience to campaign on environmental issues. Launched in October 2018, with an assembly at Parliament Square to announce a 'declaration of rebellion' against the UK Government, the group has staged regular demonstrations against current environmental policies. More than 1,000 activists were arrested in April 2019 after protesters occupied four sites across London, as well as blocking roads, disrupting a railway line and conducting a protest at Heathrow. Other demonstrations have included a semi-naked protest inside the House of Commons and blockading streets in London, Cardiff, Leeds, Bristol and Glasgow. The group says climate breakdown threatens all life on Earth, and so it is rebelling against politicians who “have failed us”, to provoke radical change that will stave off a climate emergency. The movement has become global with groups set up in countries include the US, Spain, Australia, South Africa and India. Martin Belam Photograph: Anadolu Agency/Anadolu

Police said they had 1,000 officers on the streets but were still unable to prevent roadblocks continuing at Marble Arch, Parliament Square, Oxford Circus and Waterloo Bridge.

The environment secretary, Michael Gove, said in an interview on BBC One’s The One Show that the government had “got the message” from the protesters, prompting an invitation from Extinction Rebellion for him to come to Parliament Square to discuss the crisis.

“I know one or two of the people who have been involved in organising this,” said Gove. “We’ve talked in the past and we’ll be talking in the future … I do think that some of the stuff that’s gone on has been over the top, and I do think, however, behind that is a legitimate desire to put climate change and the environment further up the agenda.”

On Thursday, Heathrow said it was working with authorities to deal with the threat of protests and the home secretary, Sajid Javid, urged the police to use the “full force of the law” to deal with the demonstrations.

Earlier in the day, Eastburn, Ovland and Watson were charged with obstructing trains or carriages on the railway by an unlawful act, contrary to section 36 of the Malicious Damage Act 1861, over the protest on Wednesday that halted Docklands Light Railway (DLR) services.

They pleaded not guilty at Highbury Corner magistrates court. The district judge, Julia Newton, denied the three bail and remanded them in custody to appear at Blackfriars crown court on 16 May. The maximum prison sentence under the charge is two years.

Thousands of people remained at the four sites on Thursday and activists hoped that more people from across the UK, freed from the constraints of work by the long Easter weekend, would also join in.

A climate activist is carried away by police on Waterloo Bridge on the fourth day of disruption in the capital. Photograph: Stefan Rousseau/PA

On Thursday afternoon, police continued to enforce their section 14 order in Oxford Circus. Under the order, protesters have been told they can continue their demonstration at Marble Arch.

The Guardian watched as police carried away one protester after another, while crowds chanted “tell the truth” and “we love you” as each demonstrator was taken away.

Emmy Stocking, 35, a landscape gardener from Bury St Edmunds in Suffolk, was handing out free food from a tent. “So far it’s just been lovely vibes,” she said. “Police have been arresting people but the atmosphere is awesome.”

It was quiet on Thursday at the Marble Arch site where activists have been camping all week. A woman played acoustic guitar and sang folk songs from the solar-powered stage while passersby visited information stands or had clothes printed with Extinction Rebellion logos.

An Extinction Rebellion demonstrator is arrested at Oxford Circus. Photograph: Jonathan Brady/PA

Actor Emma Thompson joined the protests in London on Thursday and in a video shared by Extinction Rebellion, she urged viewers to “come and join” the demonstrations.

She said she was unable to be at the first day of the protest as she was away with her husband as she turned 60.

“I absolutely wanted to be arrested on my 60th birthday but I didn’t quite manage that,” she said. However, there was some criticism that the star had flown from Los Angeles. Her representative said she had just returned home to London after working in LA.

The protests have continued despite police imposing conditions at three of the four sites where protesters have blocked traffic since Monday. Parliament Square, which was partially seized by police after they appeared in large numbers early on Wednesday evening, was retaken later the same night by protesters who arrived with a samba band and re-established roadblocks.

In Parliament Square on Thursday, protesters had reinforced their lockdown protests. One group had attached a coffin to a safety rope holding a man up in a large tree outside the supreme court. If the coffin were moved, the safety rope would fail.

Dav, 40, from Bristol, who built the contraption, said: “I learned to do this on a tree protest in Tasmania, where we were protecting old grove rain forests from logging corporations, and we have adapted it numerous times around the planet.

“This is the most lo-fi version of it I’ve done, and it just suited the need of blocking the road with just one piece of rope.”

#ExtinctionRebellion protesters have beefed up their lock down fortifications at #ParliamentSquare



This coffin is attached to a safety rope holding a man up a large tree outside the supreme court. If the coffin is moved, the safety rope will fail.#RebelForLife pic.twitter.com/qdtvuryy2N — Damien Gayle (@damiengayle) April 18, 2019

Police have come under heavy criticism for apparently targeting legal observers – volunteers who collect evidence on protesters’ behalf during interactions with officers – as they worked on Waterloo Bridge. The Guardian witnessed officers pointing out the observers, who wear orange tabards, before moving in to serve them with notice to leave.

One observer, Stu Daniel, from Devon, who was arrested on Tuesday, said he had never seen police target legal observers before. “We are impartial in our note-taking,” he said. “We aim to facilitate a peaceful arrest process for activists choosing to take that step.

“We are a strong symbol and a deterrent for the very rare but occasional occurrence of heavy-handed police behaviour and, equally, can provide a reminder were there to be any slips from [Extinction Rebellion’s] non-violent protocol in protester behaviour.”