The Conservative conference experienced its first cabinet dispute when Kenneth Clarke mocked Theresa May shortly after she suggested an illegal immigrant had resisted deportation on the grounds that he had a pet cat.

As the judiciary press office challenged the claim by May, the home secretary, Clarke said he would take a bet with her that nobody had used a cat to resist deportation.

The justice secretary told a fringe meeting organised by the Daily Telegraph: "I've never had a conversation on the subject with Theresa, so I'd have to find out about these strange cases she is throwing out.

"They are British cases and British judges she is complaining about. I cannot believe anybody has ever had deportation refused on the basis of owning a cat. I'll have a small bet with her that nobody has ever been refused deportation on the grounds of the ownership of a cat."

A Home Office source later defended May, saying she had been right. The source quoted the judge in the case, who said: "The evidence concerning the joint acquisition of Maya [the cat] by the appellant and his partner reinforces my conclusion on the strength and quality of the family life that appellant and his partner enjoy."

Clarke spoke out shortly after May told the conference she would amend immigration rules to restrict the ability of illegal immigrants and foreign criminals to resist deportation by invoking the right to a family life under the Human Rights Act. This incorporates rights enshrined in the European convention on human rights (ECHR).

May illustrated what she said were the problems with the legislation using cases highlighted in the rightwing press. "The illegal immigrant who cannot be deported because – I am not making this up – he had a pet cat," she said.

Clarke, who is due to receive a report on the future of the ECHR, said May had not consulted him before making her remarks.

"When I have found out from Theresa what these examples are that have upset her, I will probably find she agrees with me – it is these daft misinterpretations of the act which are giving the whole thing a bad reputation, when we should be a force in favour of human rights and individual liberty in the modern world, not in any way resiling from it," he said.

He launched a strong defence of the ECHR, saying: "The victorious British, who had fought fascism, actually took the lead in drawing up the European convention of human rights … This was the idea to get values established across the former fascist parts of Europe, to make sure we got back to universal European standards at least of individual liberty – the thing for which the Conservative party stands most strongly inside the British political system."

Although May promised the conference she was not making the story up, the judicial communications office, which represents senior judges, insisted the tale was not true and said it had told May's department as much.

"This was a case in which the Home Office conceded that they had mistakenly failed to apply their own policy – applying at that time to that appellant – for dealing with unmarried partners of people settled in the UK," a judicial communications office statement issued at the time of the case said.

"That was the basis for the decision to uphold the original tribunal decision – the cat had nothing to do with the decision," a spokeswoman said.

The case was one of several alleged cases the home secretary used to illustrate her claim that the Human Rights Act should go, and to justify her intention to clarify the immigration rules to ensure a right to family life is not used to block immigration deportations.

The home secretary later said she accepted the judges' correction, but argued that she was not relying on that single case to justify her policy.

Home Office sources though, challenged Kenneth Clarke's claim that no foreigner had ever resisted deportation on the grounds of owning a cat. The sources said that the immigration judge in the case of the Bolivian national highlighted by the home secretary had cited the case of Maya the cat when he ruled against deportation. This was dismissed on appeal.

A Home Office source said: "This shows why we need clarification. There is a complete lack of clarity here."

The immigration judge said: "The evidence concerning the joint acquisition of Maya (the cat) by the appellant and his partner reinforces my conclusion on the strength and quality of the family life that appellant and his partner enjoy."

The judge added: "Canadian courts have moved away from the legal view that animals are merely chattels, to a recognition that they play an important role in the lives of their owners and that the loss of a pet has a significant emotional impact on its owner."

May's speech was not shown to Clarke. In common with conference speeches by all cabinet minsters, it was cleared with the "quad" committee of David Cameron, Nick Clegg, George Osborne and Danny Alexander.

Sadiq Khan, the shadow justice secretary, said: "The energy and time this government is spending on arguments about the HRA shows how completely out of touch it is with the British people who are not interested in cat fights between ministers but how the safety of their communities will be protected after cuts in police budgets which go too far and too fast."

May also introduced Colonel Tim Collins, the Iraq war veteran, as the first declared Conservative candidate to run as a police and crime commissioner next November.

Collins set the tone for his campaign by declaring he wanted the police to be "ratcatchers and not social workers", claiming they currently gave undue preference to political correctness and that he wanted to see ex-business and ex-military figures stand as PCC candidates, not "sunset councillors or retired policemen with axes to grind".

May endorsed Collins's approach, telling delegates: "I wouldn't want to be a criminal if he gets elected."

The home secretary renewed her commitment to reforming the police, and insisted government cuts did not mean that frontline policing could not be maintained and improved.

But it was on immigration that May came unstuck. She repeated her pledge to reduce net migration to the "sustainable levels of tens of thousands", then said: "We need to make sure that we're not constrained from removing foreign nationals who, in all sanity, should have no right to be here.

"We all know the stories about the Human Rights Act. The violent drug dealer who cannot be sent home because his daughter – for whom he pays no maintenance – lives here. The robber who cannot be removed because he has a girlfriend. The illegal immigrant who cannot be deported because – and I am not making this up – he had a pet cat."

She said she was announcing the change in the immigration rules to "ensure that the misinterpretation of article eight of the European convention on human rights, the right to family life, no longer prevents the deportation of people who shouldn't be here".

The home secretary read out the wording of the article, which says the right to family life should not be interfered with except where it is "necessary in a democratic society in the interests of national security, public safety or the economic well-being of the country, for the prevention of disorder or crime, for the protection of health or morals, or for the protection of rights and freedom of others".

She said this showed that the right to family life should not be used to drive a coach and horse through the immigration system by blocking deportations.

But this definition, which has been used by judges to determine deportation appeals since Ted Heath's 1971 Immigration Act, would appear to cover all the cases of convicted foreign criminals and illegal migrant families living on benefits that the home secretary has complained about.