Greenfields Community Group argues that planning permission granted in 2018 for part of Greenfields Recreation Ground should be revoked after it was later proven that the land was held in trust for community use.
The site was sold by Shrewsbury Town Council to CSE Developments in 2017, and Shropshire Council granted planning permission the following year for 15 homes.
A judicial review concluded that while both councils had failed to establish whether the site had formed part of the recreation ground, the trust did not survive the sale and did not affect the planning permission.
The ruling was upheld by the Court of Appeal last month, when the judge in the case also refused permission to appeal to the Supreme Court.
It means the last available route to the residents is to apply directly to the Supreme Court for permission to appeal, and fund the process themselves.
Dr Peter Day, who lodged the appeal on behalf of the group, said: “What this means for our community is the loss of valuable open space, play areas for our children and a secure and safe footpath which is used by our children on their way to primary school.
“All of this is lost, not just now but also in the future for their children.
“The electors of this area have made clear that they cannot accept this unlawful disposal and that they will continue to fight.
“The whole community is behind this, both in terms of providing professional expertise, fundraising, funds and well as more simple tasks like contributing their skills.
“We are acting for and on behalf of our community.
“After a number of email correspondences and although this is difficult for our community during a pandemic, we have decided that our resolve is to continue, even without the ability to meet or fundraise as we have previously, to raise funds for a further legal campaign.
“We are asking the residents of Greenfields and the people of Shrewsbury to support our continued campaign.”
The group will this week apply to the Supreme Court for permission to appeal the Court of Appeal ruling, and has also instructed its legal team to prepare a civil case.
Dr Day added: “We believe that the long-term value of open space and loss of recreation land has not yet been fully costed.”
Shropshire Council has been asked to comment.
Meanwhile an independent review into the actions of Shrewsbury Town Council in the sale of the land is being carried out by Michael Redfern QC.
His findings are due to be published in the next few weeks.