Shadow Leader of the House of Commons Alan Duncan is under police investigation after saying he would kill US model and Miss California, Carrie Prejean, for being homophobic.

Prejean, 21, was taking part in the Miss America competition last week when she was asked by gay blogger Perez Hilton whether she thought gay marriage should be legalised in every state of America.

She responded by saying, “I believe that marriage should be between man and a woman. No offence to anybody out there, but that’s how I was raised and that’s how I think it should be – between a man and a woman.”

Prejean came second overall in the Miss America contest and later said she lost her crown as a direct result of her answer to the homosexuality question.

Alan Duncan, the gay Conservative party frontbencher, said he might kill Prejean for being homophobic, while appearing on the BBC’s Have I Got News For You programme.

Duncan, 51, appeared on Have I Got News For You on Friday night along with comedians Katy Brand, Frank Skinner and Paul Merton. He said, “I don’t agree with her [Prejean] at all… If you read that Miss California has been murdered, you will know it was me won’t you?”

A number of viewers complained to Ofcom about his comments and to the police.

Duncan said that his comments were not meant to be taken seriously, “Of course it was in jest … It is a comedy show after all. I’m sure Miss Prejean’s very beautiful and that if we were to meet we would love each other. I have no plans to kill her. I’ll send her a box of chocolates - unpoisoned,” reports the Daily Mail.

George Hargreaves, leader of the Christian Party made an official complaint to the police. He said, “Mr Duncan has crossed the line. A senior politician suggesting, even as a joke, that it is ok that Miss Prejean should be murdered for her evangelical Christian views is totally unacceptable.”

“How can we stop gun and knife crime when the man who thinks he will be the next Home Secretary makes death threats?”

It is not clear how many complaints have been received so far by Ofcom or the police.