The top Treasury civil servant has said the Conservatives’ assessment of Labour’s tax plans “should not be presented as having been produced by the civil service”.

In a letter to the Labour Party two days ago, seen by the BBC, Treasury permanent secretary James Bowler said the calculation of £38bn of uncosted spending used by the Tories “includes costs beyond those provided by the civil service”.

The letter risks undermining Rishi Sunak’s claim in Tuesday evening’s head-to-head debate that Labour’s plans would mean £2,000 of tax rises per working household.

Shadow chancellor Rachel Reeves accused the prime minister of lying.

“Labour has no plans to increase taxes on working people,” she said, reiterating that the party has ruled out increasing the rate of income tax, National Insurance and VAT.

During the debate itself, Labour leader Sir Keir Starmer dismissed the figures as “absolute garbage”.

Treasury Minister Laura Trott stood by the claims, and rejected the suggestion Mr Sunak had lied about Labour’s tax plans.

Ms Trott insisted independent analysis had identified a black hole in Labour’s spending plans.

She said: “This is underpinned overwhelmingly by Treasury analysis so if people think Labour are going to win this election they need to start saving.”

However, in a letter to Labour’s Darren Jones, Mr Bowler wrote: “As you will expect, civil servants were not involved in the production or presentation of the Conservative Party’s document ‘Labour’s Tax Rises’ or in the calculation of the total figure used … the £38bn figure used in the Conservative Party’s publication includes costs beyond those provided by the civil service.”

Mr Bowler added that he had reminded ministers and advisers that “any costings derived from other sources or produced by other organisations should not be presented as having been produced by the civil service”.

The UK’s official statistics regulator said it was looking into the Conservatives’ claim.

The Office for Statistics Regulation – which is the independent regulatory arm of the UK Statistics Authority – is investigating, but it is not known precisely how long that will take.

An investigation can be prompted by a complaint, and when an inquiry is complete, its conclusion becomes public.

A Conservative Party spokesperson said: “We were fair to Labour in the production of the Labour tax rise briefing note and used only clear Labour policies, their own costings or official HMT [HM Treasury] costings using the lowest assumptions.”

Earlier Energy Secretary Claire Coutinho told BBC Breakfast the costings had been “signed off by the permanent secretary of the Treasury” and if anything the Tory claim was “an underestimate”.

“These are brilliant independent civil servants and they would not be putting anything dodgy in there,” she said.

Former head of the civil service Lord O’Donnell said costing of opposition party policies was “one of the grubbiest processes I’ve ever been involved in” and had been carried out by both Labour and the Conservatives in the past.

He told BBC Radio 4’s World at One programme: “Ministers tell you to produce these costings on some assumptions they give you, which are dodgy assumptions designed to make the policy look as bad as possible.”

During a head-to-head debate on ITV on Tuesday evening, Mr Sunak repeatedly claimed Labour’s spending plans would mean “£2,000 in higher taxes for every working family in our country”.

The Conservatives came up with the number based on how much they say Labour’s spending commitments would cost, dividing this by the number of UK households with at least one person working. It covers a period of four years.

While Mr Sunak suggested the costings had been worked out by impartial civil servants, they are based on assumptions made by politically appointed special advisers.

The claim went unchallenged for about 20 minutes but Sir Keir later called it “nonsense”.

Asked why Sir Keir did not use the letter to rebut Mr Sunak’s attacks during the debate, Ms Reeves said the Labour leader was “really clear” that what the PM said was “utter garbage”.

She added: “I don’t think Keir Starmer expected the prime minister to lie in the debate last night”.

The £2,000 figure was first used by the Conservatives in an advertising campaign in May.