Pro-hunt campaigner Otis Ferry says supporters will cause "mayhem" for the government in the run up to the general election, in protest at the ban.
Otis Ferry says hunting for him is a lifestyle not a hobby.
The son of rock star Bryan Ferry told BBC's Breakfast with Frost he felt a "total commitment" to continue hunting.
But Education Secretary Charles Clarke said he thought predictions of trouble had been "overstated".
Police forces will get no extra funding to enforce the ban, from next February.
Instead money currently used to protect hunts from saboteurs will be used.
Speaking on the Frost programme on Sunday, Mr Ferry said he was among many pro-hunt supporters who felt strongly about the ban.
The 21-year-old was among protesters who stormed into the Commons during a debate in September this year and was arrested last year outside the prime minister's Country Durham home during a pro-hunting demonstration.
He told Sir David: "There are a lot of people who have lived the life of hunting for many more years than me. I am only 21 and I feel incredibly strongly about it."
"It is not a hobby. It is a lifestyle. It is total commitment. They can't just wake up one morning and say 'Oh, this is illegal now, sorry, what shall I do with all of these hounds and all of these horses.' It is not going to
Education Secretary Charles Clarke, a fellow guest on the programme, said he thought the extent to which people wanted to break the law would be "far less than people fear".
"I think the general desire across the country as a whole will be not to have mayhem, not to have violence, not to have all kinds of disorder in various places, and I think that will make itself felt," he said.
Senior police officers have warned that policing the ban would impose an added burden on them.
But in an interview for ITV1's Jonathan Dimbleby programme on Sunday, Home Secretary David Blunkett says the ban would be "fully enforced".
He said he expected officers to act with "sensitivity" until people get used to the change in legislation on 18 February.
"The law will have to be implemented and therefore the police will take action where and whenever they think it's necessary to do so.
"If they (pro-hunt supporters) deliberately say 'look we're going to break this law because we don't agree that our democracy, parliament, should have voted this way', then of course the police have to take action."
But Mr Blunkett said police forces would use "existing resources" which are used to protect hunts from protestors or saboteurs, to enforce the new law.
Hunt supporters have threatened a campaign of civil disobedience.
The Association of Chief Police Officers' spokesman on rural affairs, Suffolk Chief Constable Alastair McWhirter, said enforcing the an would be "an additional burden", saying forces would look to ministers for guidance.