CLEVELAND police's apparent power to ban Yarm Fair's traditional display of gipsy horsemanship, known as flashing, was challenged by councillors this week.
Alleged consent for road closures and traffic diversions through Ingleby Barwick was also questioned.
Yarm town councillors, travellers and the police recently met to discuss issues relating to the fair. But some councillors were this week unhappy with the subsequent police version of agreements at the meeting.
They also raised concerns over what exactly the police required from three risk assessments which are due to be carried out before next year's fair.
Flashing stems from the traditional sale of horses and ponies which accompanies the fair. The displays along the High Street were banned at this year's fair by Cleveland police, following an incident when a young traveller lost control of a horse.
The number of animals has risen in recent years, Yarm councillors said this week. But it hoped flashing could go ahead for a period of perhaps 20 minutes. The spectacle was popular with the public and an important Yarm tradition, they said.
At Tuesday night's council meeting, chairman Coun Liz Marsden said: "The police will only support flashing if a proper risk assessment is carried out."
Some councillors disagreed with the force's interpretation of the recent joint meeting.
Coun Marjorie Simpson said: "The police have no right to inflict their view on the parish council."
Speaking about flashing, she said: "They police look at gipsy horse riders and expect to see them wearing hats and full tack. But gipsies don't ride like that. If you watch them, you'll see that they ride deep into the horse's back and have full control. The police don't recognise that way of riding."
She doubted the police would ever agree to flashing, whatever the results of risk assessments. She also questioned a paragraph suggesting Yarm councillors had supported a plan to divert traffic from Yarm through Ingleby Barwick.
"That was wrong. To send traffic into another area would be totally unfair. We should not consider sending traffic somewhere else. It is a built-up area and if we cannot accommodate the fair traffic, we should not expect anywhere else to have it."
Coun Peter Monck picked up on another paragraph from the police record. It referred to the closure of West Street, which runs parallel to the High Street and serves as a alternative route through the town centre.
"That paragraph is appalling. What about the people who live in West Street? They won't be able to park there."
Coun Marsden said all the risk assessments would be combined and then a decision taken.
Further talks between all parties are planned for the new year.
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