Terence Maughan and Kathleen Casey live with their families on Aylestone playing fields, near Leicester, but Leicester City Council - which owns the site - wants them out and secured a possession order last month.
Mr Maughan claims conventional housing is unsuitable for him and his family because of the nomadic lifestyle in his blood.
And Mr Justice Collins, told London's High Court Mr Maughan has an 'aversion' to normal housing and 'says that bricks and mortar made him ill'.
Although there is an authorised travellers' site in the area at Meynell's Gorse, the pair's lawyers say the camp is already well over-subscribed, with around 30 families on the waiting list.
Their solicitor, Sharon Baxter, said their predicament threatened to 'wipe out' their age-old way of life. Life on the road had been 'made impossible' by the lack of official travellers' sites.
Mr Justice Collins pointed out that local authorities are confronted with 'acute problems' in trying to find appropriate travellers' sites.
But he told the court: 'There is also a concern that their way of life should be respected.'
Mr Maughan moved onto the playing fields in October last year, with the Casey family arriving in January this year.
The county council issued county court eviction proceedings on 4 February and was granted a possession order six days later.
Both families' lawyers are now seeking judicial review of the council's stance and Mr Justice Collins today granted them a 'stay' on the possession order pending the outcome of the legal challenge.
STRAN D NEWS SERVICE