David Cameron was less than fully supportive when the Labour MP Gavin Shuker asked him at Question Time today about whether he “supports” his candidate for police commissioner in Hampshire. That candidate is Michael Mates, the former MP (and once, briefly, a minister) who is probably the best-known and most colourful of all the Conservative contenders for police and crime commissioner (PCC) in November’s elections.

But the Tories are now in real danger of losing another of their PCC candidates.

Michael Mates is facing strong calls from within his own party to step down as candidate for Hampshire and the Isle of Wight over his suitability for such a sensitive job.

I have spoken to several Tory critics who hold senior positions in the party in Hampshire and in local government in the area. They feel Mr Mates is unsuitable for the role of police commissioner because of two episodes from his past. The first is his friendship with Asil Nadir, the businessmen who got ten years jail last month for fraud, and for whom Mates acted as a defence witness at the Old Bailey.

The other reason is a windfall, estimated to be worth around £40,000, which Mr Mates received around 2006 from his tenancy of a flat in Dolphin Square, Westminster. This was compensation by the owners of the freehold of the property to give up his tenancy. Mates’ rent on Dolphin Square, where he had been a tenant since the 1970s, was paid from his parliamentary allowances – ie. It was public money.

One critic, Graham Burges, the deputy leader of Gosport Borough Council, said: “I believe the candidate for police and crime commissioner should be beyond reproach and this candidate still has some questions to answer.

“In relation to Dolphin Square he should have paid back the money straight away. Its too late to do it now.

“I believe he should stand down and I have been contacted by many Hampshire members who have expressed a similar view.”

Mr Mates was one of 42 MPs to receive such windfalls, and the parliamentary standards commissioner John Lyon has stated in the cases of many of those MPs (though not all of them), that a large share of the windfall should be paid back to Parliament.

Mr Mates has not yet paid any money back to the Commons authorities. He says that when he left Dolphin Square he reinvested his windfall in a house in London, and did so with the approval of the then parliamentary authorities, the Fees Office. Mr Mates said some years ago (while he was still an MP) that he would seek further advice on what to do about his windfall when he finally left the Commons.

Mr Mates stepped down as an MP at the 2010 election, but has yet to seek advice from IPSA, the body which now handles MPs’ expenses.

Mr Mates tells me his London home is now on the market and he has found a buyer for it. He says that once the property has been sold he will seek advice from the parliamentary authorities, and comply with whatever they advise about the windfall he received.

Mr Mates says he has “nothing to hide” though he refuses to say what the amount of his Dolphin Square windfall was.

The Labour front-bencher Gavin Shuker asked David Cameron today: “Does the Prime Minister have full confidence in his Police and Crime Commissioner in Hampshire?”

Cameron replied: “We havent yet had the elections; the elections are in November. This is a good opportunity to broadcast from this House what an important set of elections they are. I want to see a new form of accountability coming through our police forces and I think it’s an excellent reform and I’m sure one that many people want to turn out and vote, and vote for their local Conservative candidate.”

Less than fulsome praise for Michael Mates, on the day when his Hampshire critics went public with their discontent.

Follow @MichaelLCrick on Twitter.