Shadow Home Secretary Yvette Cooper has admitted she thinks the Labour Party will soon have a female leader.

In an interview with The House magazine, she said: “I think it will [be natural] for all parties. You do see over time more ceilings are smashed.”

Cooper dismissed speculation of her own leadership ambitions, saying Ed Miliband was doing a “really good job”.

She admitted that she was not happy in her current job. “That’s because I want to be Home Secretary in a Labour government, that’s the job I want to do.”

She said it was not worth discussing who would replace Miliband because: “We will learn the lessons of what happened with the Labour party with Gordon and Tony when everybody was speculating always about the future. Actually that is the wrong way to do things”

Cooper rubbished reports about a “lasagne plot” hatched by her and her husband, Ed Balls, to unseat Ed Miliband as leader.

She refused to say whether her daughter had said, “my mummy’s going to have that job [of leader]”.

“You know, we don’t talk about the kids, whatever they say” she said.

The shadow home secretary also expressed sympathy for her opposite number, Theresa May.

"I strongly disagree with her in terms of strategy but I’ve got huge respect for what she’s done as a woman to get to the top of the Tory party at a time when there’s actually been so few women," she said.

“We were both elected in 1997 at a time when although there were quite a lot of Labour women who were elected at that time, the Tories there were very few of them. There was Theresa, there was Eleanor Laing. I think she has probably had a very difficult time over many years as a result of that. And it’s just outrageous that she still gets more comments on her jackets and her shoes than on policy things.

“I have huge sympathy for her dealing with the Tory party. And I actually do wonder whether David Cameron does actually listen to her. Because she got a bad deal in the spending review and William Hague got a better deal in the spending review.”