A community project set up to protest against a third runway at Heathrow has been given 14 days to leave its home by the high court.

Grow Heathrow took over a derelict garden centre in Sipson in 2010 and turned it into a community garden as part of action in protest against the plans for the runway. About 20 people live at the site and from their base they have become an integral part of the community activity against the building of a third runway at the airport.

But on Thursday Judge Dight granted a possession order to the landlords of the site, Lewdown Holdings. The judge acknowledged the hardship and logistical difficulties which will be caused by the effect of the order which requires the eviction of an entire settled community, but granted Lewdown the possession order.

Lawyers for Grow Heathrow argued they had the right to a home, as interpreted under Article 8 of the Human Rights Act 1998 and were therefore entitled to resist a possession order. Any possession order, they said, would infringe the freedom of expression (under Article 10) and freedom of assembly, protest and association (under Article 11).

The judge found that the defendants could not rely on these rights to override Article 1, that: “Every natural or legal person is entitled to the peaceful enjoyment of his possessions.” The judge stated that a “private landowner [is] entitled to put its land to any form of lawful use, including doing nothing with it”.

He said the owner had no need to justify his alleged failure to use the land for any purpose.

Alex Sharpe, one of the protesters, said Grow Heathrow would appeal against the granting of the order. He said: “What we want to do now is sit down with the landowners Lewdown and talk to them like adults. They have had their planning permission for this site rejected and we don’t have any intention of leaving this site. We hope to be able to talk to them sensibly about this.

“We don’t have any intention of leaving the Heathrow villages because we are part of the fight against the third runway, and as long as that is still a threat we will be here.”

The activists are being given pro bono legal help from Leigh Day.

The eviction of the residents could start in 14 days, but activists hope the appeal and conversations with the owners will mean this does not happen.

Ruth Raynor, one of the Grow Heathrow protesters, said after the hearing in London: “We are completely committed to continuing support for the local community. Airport expansion will make their homes uninhabitable.

“As caretakers of this land we’ve cleared 100 tonnes of rubbish, returning the land to an ecological habitat and community garden. We would like to continue a conversation with Lewdown Holdings outlining a community based educational project.”

The shadow chancellor and Labour MP for Hayes and Harlington, John McDonnell, said the project had inspired the whole community and improved what was a derelict site. “We need lawful spaces of protest with the values of education and community embedded in them; Grow Heathrow would be a great loss for my constituency in this crucial campaign year against Heathrow airport’s expansion,” he said.

The activists and their hundreds of supporters cleared the site of 30 tonnes of rubbish and built a self-sufficient community when they took over the site in 2010 as part of protests against the third runway.

Jane Taylor, chair of Harmondsworth and Sipson Residents Association, supported the activists.

“Grow Heathrow came to the village to breathe new life into the community following another attempt by Heathrow airport to decimate its neighbouring villages. They took over a piece of neglected land which they skilfully rejuvenated to provide a vibrant hub for like-minded people.”