Theresa May has criticised the BBC for paying women less than men for doing the same job and insisted the organisation must continue publishing its top salaries to prove it is tackling the problem.

Documents setting out the pay for staff on more than £150,000 showed a shocking gap in the earnings of the corporation's most well-known male and female presenters and actors, with Radio 2's Chris Evans topping the list on more than £2 million while the highest paid woman was Claudia Winkleman on between £450,000-£499,999.

Mrs May said it was important the BBC "looks at the whole question of how they pay women and how they pay men for doing the same job".

She told LBC: "I think what has happened today is we have seen the way the BBC is paying women less for doing the same job as the men.

"I want to see women paid equally with men. The only reason we know about this though is because the Government required the BBC to publish these figures.

"The Director-General, Lord Hall, has said that he wants to change this, he wants to make progress, he wants to abolish this gender pay gap.

"We want to see him doing that too. I think it is important the BBC carries on publishing figures in the future so we can see the progress they are making."

Labour indicated BBC stars such as Gary Lineker could face significant pay cuts if Jeremy Corbyn becomes prime minister.

A party source confirmed that Labour's promise of a maximum 20 to one ratio between the highest and lowest paid staff in public sector organisations would apply to those directly employed by the BBC.

Mr Corbyn made no comment on BBC salaries during the final session of Prime Minister's Questions before the summer recess, when he concentrated his attack on the Government's record on low pay.

But a source later told reporters that policies in Labour's manifesto designed to tackle income inequality - including the maximum pay ratio in the public sector, a higher income tax rate for the top 5% of earners and an excess pay levy on organisations with staff on more than £330,000 - would apply to the BBC.

Stars employed indirectly through independent production companies would not be caught by the pay ratio, he said.

The source also said that the gender pay gap exposed by the BBC figures was "obviously wrong", adding that Labour was "committed to gender equality audits enforced through law".

Conservative former minister Anna Soubry said it was "a disgrace" that the BBC was required to disclose salaries and she could not defend Tory policy on the issue.

The Broxtowe MP told BBC Radio 5 Live Daily's Adrian Chiles: "This story is a disgrace, not because of figures but the fact that it's ever been published.

"I take objection on behalf of these people who have had their names and their salaries exposed in this completely undignified way.

"What this will do is that it will stoke up the politics of envy... People will say, well, why is a nurse worth less than Gary Lineker or Chris Evans, and that's a completely meaningless debate.

"So the BBC should be ashamed of themselves, they should never have agreed to this, it shouldn't have been done."

Labour's shadow culture secretary Tom Watson said: "The BBC is one of the world's greatest broadcasters and we shouldn't be surprised that its top stars - who millions of people tune in to watch and listen to every week - are well paid.

"Labour recognises the BBC's dilemma: the need to give licence payers value for money while operating in a competitive commercial environment against other broadcasters who do not have to disclose what they pay.

"It's wrong that only a third of the BBC's highest paid stars are women, and we welcome Lord Hall's commitment to close the gender pay gap by 2020. It would be good to see a similar commitment, and similar levels of transparency, from other media organisations - especially those who are criticising the BBC today."

Liberal Democrat deputy leader and former equalities minister Jo Swinson said the figures on the gender pay gap should act as a "really strong wake-up call".

"We need to eliminate the gender pay gap as quickly possible," said Ms Swinson.

"Making gender pay gap data transparent is vital to pierce the bubble of complacency in organisations. That is why I was so determined in 2015 to win the fight in government to introduce mandatory gender pay gap reporting.

"That means that not only do we know the picture in the BBC, soon we will be able to see how other media organisations compare."

Presenter of BBC Radio 4's Today programme John Humphrys, who earns between £600,000-£650,000, suggested he could cut his salary in half if asked to do so by the broadcaster.

Pressed on whether he would work for less money, he told the BBC: "I have taken a couple of sizeable, very large, very sizeable pay cuts just recently. How much? I don't know.

"See what the BBC wants me to do. Would I chop my salary in half? Maybe I would, I don't know. The BBC hasn't suggested it."