Rishi Sunak was today facing questions over a possible breach of the ministerial code, after it emerged he told David Cameron in a private text message he had “pushed” Treasury officials over the ex-prime minister’s requests for help for ailing finance firm Greensill.

Labour demanded a “full, transparent and thorough investigation” into the company’s links at the highest levels of government, saying that the message suggested Greensill received “accelerated treatment and access to officials”.

The comment emerged in a text message released by the chancellor in response to a freedom of information request.

Mr Sunak also confirmed that Mr Cameron lobbied two other Treasury ministers “informally” as he fought unsuccessfully to get access for Greensill to government Covid support.

The Treasury said that the two texts from Sunak released today represented “all messages that were sent from him to David Cameron” on the Greensill issue.

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But they said that the former PM’s communications to Treasury ministers were not being made public, as they were sent “in his capacity as an employee of Greensill and with an expectation of confidence”.

In the first text sent on 3 April last year, just weeks after he was appointed chancellor, Mr Sunak said: “Hi David, thanks for your message. I am stuck back to back on calls but will try you later this evening and if gets too late, first thing tomorrow. Best, Rishi.”

But in the second, sent on 23 April, Mr Sunak went into more detail about Mr Cameron’s efforts to persuade the Treasury to amend the terms of its support scheme so Greensill could be included.

“Hi David, apologies for the delay. I think the proposals in the end did require a change to the Market Notice but I have pushed the team to explore an alternative with the Bank that might work. No guarantees, but the Bank are currently looking at it and Charles should be in touch. Best, Rishi”.

The text referred to discussions with the Bank of England, involving the Treasury’s second most senior civil servant Charles Roxburgh, in relation to the notice setting out the terms of the government’s new Covid Corporate Financing Facility (CCFF).

A memo released by the Treasury last month revealed that Mr Roxburgh spoke to an unidentified Greensill representative by phone on 24 April – the day after Mr Sunak’s text.

He said that the the Treasury was “still working through the design questions” for the scheme with the Bank and may want to do some “confidential market testing” with the company and other stakeholders. The Greensill representative was recorded as saying they were “very pleased to hear this news”.

Shadow chancellor Anneliese Dodds said: “These messages raise very serious questions about whether the chancellor may have broken the ministerial code.

“They suggest that Greensill Capital got accelerated treatment and access to officials, and that the chancellor ‘pushed’ officials to consider Greensill’s requests.

“The chancellor’s decision to open the door to Greensill Capital has put public money at risk. There must be a full, transparent and thorough investigation into the chain of events that saw Greensill awarded lucrative contracts, the freedom of Whitehall and the right to lend millions of pounds of government-backed Covid loans.”

A Treasury source “very, very strongly” rebutted any suggestion that Mr Sunak’s use of the word “pushed” meant he had been putting pressure on officials to make Mr Cameron’s proposals work.

The source said Mr Sunak had merely been asking his team to look at alternatives being put forward, and noted that “multiple” messages from the ex-PM had gone unanswered.

The company eventually filed for insolvency after failing to secure support through the government’s Covid Corporate Financing Facility.

Scottish National Party MP Stewart Hosie said the texts revealed that “Boris Johnson’s Tory government is stumbling from one scandal to the next”.

He said: “Tory ministers and former prime ministers casually texting each other over government access utterly reeks.

“When MPs return from recess, Rishi Sunak must come before Parliament and set the record straight over his full exchange with David Cameron and what the outcome of those messages were.”

Mr Cameron has maintained silence since news broke last month of his involvement in lobbying government on Greensill’s behalf. He was cleared by a regulator of failing to register as a lobbyist, on the grounds that he was an employee of the supply chain finance specialist.

Labour has previously called for an investigation by the Committee on Standards in Public Life over reports that the company’s founder Lex Greensill – a former colleague and friend of ex-cabinet secretary Jeremy Heywood – was given a government desk and pass and given access to a number of Whitehall departments in his role as an adviser.