An official Whitehall report into Damian Green’s behaviour might never be published, prompting fears of a cover-up, it has emerged.

Mr Green – the de facto deputy Prime Minister - is fighting to save his political career after being accused of making inappropriate advances towards Kate Maltby, a writer who is 30 years his junior.

Mr Green, the First Secretary of State, is also facing claims that pornography was found by police on an office computer he used in 2008.

Theresa May, the Prime Minister, asked Sir Jeremy Heywood, the Cabinet secretary, three weeks ago to “establish the facts and report back as soon as possible” about the claims.

The investigation and report - which is being written and prepared by Sue Gray, the head of propriety and ethics in the Cabinet Office - is now expected to be completed next week and handed it to Mrs May, who will decide whether, and in what form, it can be made public.

There are already fears that the Government will seek to publish the report on a busy news day to lessen its impact.

The conclusions of a similar Cabinet Office inquiry in 2011 into Liam Fox when he was defence secretary in David Cameron's Cabinet were made public. He resigned days later.