The new chief executive of the Countryside Alliance has ruled out another mass march through the streets of London, despite a repeal of the hunting ban looking as distant as ever.

Alice Barnard said there were "other ways of connecting" with the media, the public and with the MPs who have not yet been given a timetable for the all-important vote on whether to even hold a debate on the Hunting Act.

Since the election in May, both sides of the hunting debate have been lobbying the new intake of MPs after the Prime Minister promised a free vote on the hunting ban.

Last week, the Western Daily Press revealed the first to declare themselves the victor in the battle for the hearts and minds of those MPs were the anti-hunt League Against Cruel Sports, who said they had the support of almost 320 MPs, while the Alliance lagged behind with little more than 250.

Yesterday, the LACS dealt another blow with a YouGov poll – using the alliance's own questions – which found that three-quarters of people wanted the ban on hunting properly enforced.

Now Ms Barnard, 33, who took over running the Countryside Alliance after previous chief executive Simon Hart was elected as a Tory MP, said she was confident their plans for a Hunting Regulatory Authority would sway wavering MPs.

"It will be like FIFA. It will have a set of guidelines and authorities. Hunts will have to answer to it," she said.

"Hunting should not be one of the top economic priorities, however, it is a bad piece of legislation.

"The Hunting Act has not saved a single fox's life. Every time a hunt goes out it does so under the threat of prosecution. They endeavour to follow the law.

"But should an accident happen and it be deemed that you did not follow the exemptions you will be taken down to the police station.

"Law abiding people are being accused of a criminal offence. Should we be in a situation where we think that's acceptable? I don't think Britain is that sort of country.

"Something should be done to address this and not criminalise. If hounds are already running and hunt staff are not there then accidents do happen."

The pro-hunt lobby is now in a quandary over whether to gamble and press for a vote they might then lose, or dig in and keep lobbying for the long run. But Mrs Barnard said whichever option was chosen, the prospect of 300,000 people marching through central London as they did in 2002 was not going to happen.

"I think we did marching, and we did it really well, but we need to be looking at other ways at connecting both with Parliament, the media and the general public and of course our members," she said.

"All those people who marched are still out there and they are still supporting us. We are incredibly lucky to have a very strong membership and hugely strong support out there, right across Britain. But times change, and we are moving on."