The editor of the flagship Today programme on Radio 4 has accused Boris Johnson of a “Trumpian” attempt to undermine the BBC after he banned ministers from appearing on the show.

Sarah Sands said the move was designed to “delegitimise” the broadcaster, likening it to the president’s notorious attacks on the US media to neutralise criticism and fire up supporters.

“What’s happened is that you can see the government won a big majority,” said Ms Sands, who has edited Today for nearly three years.

“It sees Labour in disarray and it thinks it’s a pretty good time to put the foot on the windpipe of an independent broadcaster. So the strategy is quite Trumpian: to delegitimise the BBC.”

Downing Street has refused to put ministers up for interview on Today since the election win, after key aide Dominic Cummings said he “never listened” to it.

No 10 sources have dismissed the show as “irrelevant” and an example of the BBC’s focus on a “pro-Remain metropolitan bubble in Islington”.

Earlier this month, one said: “The Today programme is irrelevant – it is not a serious programme any more so we are not going to engage with it. It is far better for us to put people up on BBC Breakfast and 5 Live.”

The government has also launched a review into decriminalising non-payment of the licence fee, which could cost the corporation £200m a year.

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But Ms Sands claimed that individual Conservative ministers were “rather puzzled” by the boycott and wanted to appear on her programme.

She predicted that “peace would break out” with Downing Street after Christmas – while noting that many listeners felt the programme had improved with wider reporting and analysis.

Ms Sands also denied that Today spoke to a pro-Remain bubble, highlighting its election coverage from Leave-backing towns such as Crewe, Wigan and Barnsley.

Ken Clarke, the former Conservative chancellor, has called on Mr Johnson to sideline Mr Cummings, who is thought to be behind the Today boycott.

He said he should “shunt aside” those aides who had helped to secure his return to Downing Street, and warned that his administration could be undone by hubris.

“Don’t think you are walking on water, don’t think you are untouchable. You can make a big mess of it,” he told Pienaar’s Politics on 5 Live.

Ms Sands argued that, under her leadership, Today had enhanced its arts coverage and broadcast entire programmes from universities.