The BBC could axe half its website, sell magazines, close two national radio stations and cut spending on imports in a major strategic review produced by the corporation's director of policy and strategy, John Tate, and reported by The Times.

You would think that a story headlined "BBC signals an end to era of expansion" would be like all News Corp's dreams come true. But actually it's not enough for the Murdochs. The Times' leader - headlined "Big, Bloated and Cunning" - declares:

"If the BBC were serious about reform it would consider selling Radio 1 and getting out of the pop music business, which is hardly ill served by others. It would give up BBC Three, which has no rationale at all. It would get tough on executive pay, and admit that it cannot continue to be regulated by a trust that is also its cheerleader. "The new proposals were written to serve the best interests of the BBC, not the public. The next government will need to take on what Channel 4's chairman last year described as "the most powerful lobbying and effective organisation in Britain". Until then, Auntie Beeb's warm embrace will simultaneously be a stranglehold that is unpleasant and untenable."

Tate, a former head of the Conservative Party policy unit, is proposing (and at this stage it is a proposition, because the BBC Trust has not yet decided what to do with the plan):

• Selling BBC Worldwide's magazines . It is unclear if this would involve the whole collection - including Radio Times and Top Gear - being sold to another publisher, or a piecemeal sell-off. Commercial rivals would love to get their hands on the money-spinning magazines, but it could be argued that these are actually linked to core Corporation output. It is a sell-off of the less obviously branded magazines such as olive that would make more sense.

• Halving the size of the BBC's website. The report says that BBC Online's budget and staff numbers should be cut by a quarter, which begs the question about how the website would be cut in half. Maybe it is the total number of pages that is to be cut. This is a particular News Corp bugbear, providing excellent free web coverage that Rupert Murdoch would like to charge for.

• Closing 6Music. 60,000 people have already signed an online petition to save the station, which has already been reported as being under threat. #saveBBC6Music is trending on Twitter. And powerful licence-fee payer protest groups can twist the BBC's arm. In the old days it was Archers and Radio 4 fans. Maybe today it is the Twitteratti and 6Music fans. The amount of money involved in this would be relatively small beer in the scheme of things.

• Closing BBC Asian Network. Axing the Asian specialist station has also been trailed: it is expensive in terms of spending per listener, but it also reaches out to an audience not otherwise well-served by the Corporation. Would the commercial market be able to attempt something so ambitious?

• Cap sports spending at £300m. This would still allow the BBC to do most of what it already does - the marquee events such as the World Cup and the Olympics (which are protected events), enough football for general interest - but stop it from encroaching onto the territory that Sky "owns". It might mean the end of Formula 1 on the BBC, which would appease ITV, although whether they could afford it now is an interesting question. It would probably mean that Sky kept cricket, alongside its vast Premier League football output.

• Reduce the £100m spent on foreign imports. If the BBC cut £25m from this budget, as is proposed, what would it drop? Mad Men? Channel 4 would like that. Heroes? Sky One might snap that one up. Endless foreign films? Helps fill up hours of schedule.

As the best-funded broadcaster in Britain, while its commercial rivals are under enormous financial pressure, the BBC is an easy target for criticism of its ambitions and sprawl. The BBC plan is clearly to show that it is willing to limit its spread into the commercial world.

But if the BBC can't satisfy News Corp today, then what chance does it have of satisfying the (probable) next government? If Labour wins the spring election, they would certainly be satisfied by the proposals. But a future Conservative government's position is slightly harder to call. For all of the Daily Mail's bluster, the Tory heartland voters are also licence-fee payers who watch and love Auntie Beeb. Meanwhile the Murdochs are whispering in David Cameron's ear and they want the BBC slashed back.

If the BBC was also to throw in some more cuts, such as executive pay cuts, would it be enough? Or does it face a cut in the licence fee under the Tories?