David Cameron will not be able to win a majority at the next election because he has failed to woo ethnic minorities, Britain's first female Muslim Cabinet minister has warned.

Baroness Warsi - who dramatically resigned this week over the Government's "morally indefensible" policy on Gaza - said Tory bosses were ignoring "electoral reality" by relying on white voters.

In an interview with the Sunday Times and Independent on Sunday, the peer also lashed out at "bitchy" colleagues who questioned whether she was up to her job, suggesting that Mr Cameron's inner circle did not understand those who had not gone to public school.

"I will be out there, vocally fighting for an outright Conservative majority," Lady Warsi said. "But the electoral reality is that we will not win outright Conservative majorities until we start attracting more of the ethnic vote."

Lady Warsi said that when she was one of Cameron's earliest supporters in 2005 she thought: "This is a guy who gets today's Britain. He's a new kind of Conservative. He's comfortable with today's Britain".

But she added: "I think the party has shifted since then. The party leadership has shifted since then. I think over time it will be a regressive move because we have to appeal to all of Britain, not just because it's morally the right thing to do... but because it is an electoral reality.

"We've probably left it a little too late to take this part of the electorate seriously."

Former Foreign Office minister Lady Warsi called on the Government to "recognise Palestine as a state" and impose an arms embargo on Israel.

And she attacked Chancellor George Osborne and Chief Whip Michael Gove for failing to use their "very, very close" relations with the Israeli Government to defuse the crisis.

"What is the point of having that strong relationship if you can't use it to move them to a position which is in their interests and our interests?" she said.

Dismissing Mr Osborne's claim that her resignation had been "unnecessary", she said: "My actions would not have been necessary if he had done what he should have done, which is pick up the phone to people he is incredibly close to and say: 'It's unnecessary for you to meet your ends by taking out power stations, taking out homes, taking out schools and killing kids on beaches'.'"

Lady Warsi said the lobbying operation by Israel was "incredibly effective".

"I congratulate the Friends of Israel and those who lobby on behalf of Israel because they are incredibly effective," she said.

"I don't blame the lobby, I blame the politicians. If you are not capable of being able to decipher between lobbying and fact, and if we are incapable of politicians to see both sides of the argument, then that's a fault that we have."

She added: "I sincerely hope that how the Tory Party raises its funds does not have an impact in relation to its policy in Government. The national interest should never be subject to the chequebooks of anybody."

Rounding on criticism of her exit from the Cabinet and performance as a minister, she said: "Some of the bitchiest women I've ever met in my life are the men in politics.

"I am a brown, working-class woman from the North. People have been telling me I'm not good enough since the day I was born."

In a reference to Mr Cameron's inner circle, she added: "I don't hold the fact that someone went to public school against them. I don't hold the fact that they haven't had the breadth of experience that some of us who didn't go to public school have had.

"I hope that if I can be so understanding about their background and shortcomings, they can be understanding to those of us who haven't had those opportunities."