Senior Conservatives in the cabinet are split over how to vote in the Commons on Monday as a move to ban smoking in cars with children is expected to be passed with Labour support.

David Cameron, citing the need to visit flood-affected areas, is likely to be absent from the House. The health secretary, Jeremy Hunt, backs the ban, but his colleague, the justice secretary, Chris Grayling opposes it.

Divisions in Tory and Liberal Democrat ranks mean the measure will be supported by the Commons, ensuring it becomes law. Michael Gove, the education secretary, is supporting the ban, but the deputy prime minister, Nick Clegg, and the business secretary, Vince Cable, have said they oppose it on libertarian and practical grounds. Clegg has said he does not see how such a ban could be enforceable, the position adopted by Grayling as lord chancellor.

The communities secretary, Eric Pickles, is another sceptic. Last week he raised questions over what happens when a car is stopped with children and a smoker inside, and whether it is different from smoking at home. "We should make things criminal if we feel that they are enforceable," he said.

No 10 insisted it was not seeking to enforce any line, even surreptitiously, as the government sometimes seeks to do on nominal free votes.

Health professionals have been lobbying MPs to support the ban ever since peers narrowly agreed to support a ban on smoking in any car with children younger than 18 in it. The amendment was inserted into the children and families bill.

Health specialists have been co-ordinated by Dr Nicholas Hopkinson, from Imperial College London, who is chairman of the British Thoracic Society's chronic obstructive pulmonary disease specialist advisory group.

He said: "This letter issues a powerful statement from the medical professionals of this country - the people who, every day, are treating illnesses brought on by secondhand smoke in children - about the rights of children to breathe clean air that won't make them sick."

Simon Clark, director of smokers' lobby group Forest, said: "Smoking in cars with children is inconsiderate but there is a line the state shouldn't cross when it comes to dictating how people behave in private places."

The shadow public health minister, Luciana Berger, said 300,000 GP appointments every year result from children suffering from the effects of secondhand smoke, including young people who have had to endure passive smoking in the back of a car. "Children are especially vulnerable to secondhand smoke as they have smaller lungs and faster breathing rates than adults," she said.