But a consultation on the proposed enlargement of the Designated Drinking Area Order, which already covers most of the town centre, also revealed an appetite amongst interested parties to include Park Street, Cuttlebrook Nature Reserve and the Phoenix Trail into the extension plans.

The orders confer discretionary powers onto police officers to demand an individual stop drinking alcohol in public and to surrender their drink - with failure to co-operate potentially resulting in arrest.

South Oxfordshire District Council first designated parts of Thame town centre non-drinking areas four years ago.

Cllr Dorothy Brown, cabinet member for Community Safety, said: "This has reduced the number of adult drinkers in the town centre which has in effect made people feel safer and less intimidated."

But she admitted there had been side-effects from the orders, by moving the problem to neighbouring areas.

"We know that there has been some displacement of adult drinkers into Elms Park and Southern Road recreation ground, and we have consulted locally to find out how people feel about an extension into these areas," she said.

"The next step is to review the 11 responses to the consultation and use these along with evidence to inform our final decision. The council will then make a decision as to which areas should be covered within the next few months."

Thame Town Council's Planning Committee has welcomed the extension, but is disappointed that Park Street had not been included, because of the presence of the Sainsbury's store.

Statistics show that incidents of anti-social behaviour in Thame, which includes drink-related offences, has risen sharply in the past three years, from 137 incidents in 2005/6 to more than 400 from April 2007 to March this year.

However, chairman of the town council's planning committee, Cllr Don Butler, said: "The vast majority of adults and youngsters are very law abiding. These orders are necessary only for a small minority of people."

Neighbourhood officer for Thame, PC Russell Hounslow, said: "We did have a horrendous problem before the orders were enforced, with lots of complaints from shopkeepers especially in the vicinity of the Co-op, town hall and Greyhound walkway, but since they have been imposed the problems have been virtually eliminated from the town centre."

He welcomed the extension of the orders into the parks.