David Cameron repeatedly pushed the Bank of England and the Treasury to risk up to £20bn in taxpayer cash to help Greensill Capital, just as the lender started to face “significant” financial pressure at the start of the pandemic.

The UK’s central bank was urged to provide support to Greensill, including by setting up a fund that would buy loans made by the financial services company and its competitors, in a string of emails to senior officials.

In one, Cameron introduced Greensill’s founder to one of the Bank of England’s four deputy governors, Jon Cunliffe.

The exchanges, published by the Bank of England on Thursday afternoon, became increasingly desperate in tone as requests from Greensill for government backing were turned down.

Cameron described the situation as “incredibly frustrating” and complained: “I must be missing something here.”

Late on Thursday, the Treasury released details of a call between Cameron and John Glen MP, the economic secretary to the Treasury. In the readout, copied into top officials, Cameron is said to have argued that supporting Greensill would be “the most effective” way to help the small and medium businesses that relied on it for finance.

The Treasury has also released new text messages between Cameron and Glen, where Glen says the Treasury had decided not to extend the funding to Greensill, but offers a “private call” to explain the decision. The Treasury said it would not be releasing Cameron’s texts to Glen, because of his expectation of privacy.

The disclosures underline the concerted efforts made by Cameron to promote Greensill – approaching ministers, civil servants and officials – over a period of weeks.

In other developments in the deepening lobbying scandal:

*  MPs were told the beleaguered former prime minister had personally lobbied the Treasury’s most senior civil servant, Sir Tom Scholar, and secured nine meetings with another of the department’s key officials.

Scholar, the Treasury’s permanent secretary, told the public accounts committee the former prime minister called and sent “some text messages” to demand help for Greensill.

*  The Cabinet Office launched an investigation into leaked texts from Boris Johnson’s phone to the billionaire James Dyson. He promised to “fix” a tax issue as the company pitched to develop ventilators at the height of the pandemic.

Tory insiders and former officials told the Guardian that informal text communication for government business is commonplace, and has been for several years.

The Bank of England correspondence, released as part of a freedom of information request, shows for the first time the pressure that the former prime minister and his colleagues exerted on central bank officials.

At the time, Greensill was attempting to lobby for access to the government’s largest Covid-support scheme, the Covid corporate financing facility (CCFF), which Greensill ultimately did not quality for.

Cameron and Greensill’s founder and chief executive, Lex Greensill, contacted the bank at least seven times in March and April 2020, even corresponding with officials during weekends, after gaining direct access to Cunliffe, who is the bank’s deputy governor for financial stability.

Greensill, a supply chain finance specialist, collapsed in February after an Australian insurer refused to renew guarantees underpinning billions of dollars of loans it had made to customers.

Those loans, for which Greensill collected a fee from the borrower, were then bundled up and sold on to other investors.

The precarious arrangement was described as a “Ponzi scheme” by MPs on Thursday, as they grilled Treasury officials as they opened their inquiry into the Greensill lobbying scandal.

On 16 March 2020, after introductions by Cameron, Lex Greensill sent Cunliffe a letter asking for government backing.

Greensill pitched the idea to the Bank of England as an opportunity to get money directly to small business borrowers. With a government-backed fund to support it, Greensill would also be free to issue more loans.

“In current markets, investors are unsettled and seeking redemptions. It is critical to stabilise the supply chain finance investor base at a matter of urgency,” Greensill said in the letter addressed to Cunliffe.

“In our judgment, the initial size of the facility needs to be in the order of £10-20bn if it is to provide the necessary level of confidence to the capital markets that will ensure effectiveness in this extraordinary time,” Greensill added.

A briefing note produced by the Bank makes it clear that Greensill was facing financial pressure, due to market turmoil, when the government guarantee was requested. The notes detail a call on 17 March 2020 between Bank officials, Greensill and Cameron.

Greensill and Cameron were ultimately directed to the Treasury, which had final authority over the scheme. But Cameron continued to lobby the Bank of England for a change in rules. The former Conservative leader, who held stock options in the business, and was a paid adviser, emailed Cunliffe again on 3 April, saying he had numerous conversations with the Treasury but “failed to get anywhere”.

Cameron wanted a change in the CCFF mandate, that would allow the Bank of England to buy bonds linked to supply chain finance. The former prime minister appears to have become exasperated by the refusal of officials to change policies to accommodate Greensill.

“Why are we potentially cutting off a market that already pumps cheap credit directly into SMEs [small- and medium-sized enterprises]?” he said in an email to Cunliffe. “I think I must be missing something here. Am obviously talking to HMT [Her Majesty’s Treasury], but would be grateful for any light you could shed on this … All good wishes. Dc.”

He followed up three weeks later, saying the failure to push through changes to the CCFF – in a way that would mirror a similar scheme in 2008 – were “incredibly frustrating”.

While Greensill was ultimately rebuffed in its efforts to access the CCFF, it was later accredited to offer government-backed loans through the second-largest government-backed loans scheme in June 2020.

The shadow chancellor, Anneliese Dodds, said: “We need to follow the money. Greensill was carrying the begging bowl from the Bank of England to the Treasury and back.

“The chancellor can’t keep ducking this. He must come out of hiding and explain his role in the return of Conservative sleaze,” she said.

A spokesperson for David Cameron said: “Greensill were not asking for a government loan or direct support in any way. The Treasury letter rejecting the proposals in June makes clear that Greensill reported that market conditions were improving. So the idea that Greensill was in difficulty at that stage is nonsense.”

Key extracts from emails between David Cameron, the Bank of England and Greensill

Britain’s deputy governor of the Bank of England, Jon Cunliffe.

5 March 2020: email from David Cameron to the Bank of England deputy governor, Jon Cunliffe

“I do a lot of work with Greensill Capital, now the world leaders in this space. We would be keen to help … Do you have a moment for a quick word? I am on my old number or can call you whenever convenient. All good wishes. Dc.”

5 March 2020: email from David Cameron to James Benford, private secretary to the governor

“The purpose of this email is to introduce you to Lex Greensill, founder and CEO of Greensill Capital (GC)... I am an adviser to the company. We would be keen to step and help during the current difficulties. Perhaps a first stage would be for Lex and/or some of his team to meet with some of your experts to discuss how the market works and the role of GC within it.”

3 April 2020: email from David Cameron to the Bank of England deputy governor, Jon Cunliffe

“Jon, Am writing to ask for your help. Greensill – who I work with – have had numerous conversations with HMT but have failed to get anywhere.

The request is simple – please include in the CCFF the ability to purchase bonds issued in respect of supply chain finance. These allow us to pump billions into SMEs, (including every pharmacy that works with the NHS).”

“Why are we potentially cutting off a market that already pumps cheap credit directly into SMEs? I think I must be missing something here. Am obviously talking to HMT, but would be grateful for any light you could shed on this …”

22 April 2020: email from David Cameron to the Bank of England deputy governor Jon Cunliffe

“Apologies for bothering you about this again. We (Greensill) have had lots of conversations with HMT and while every question seems to have been answered, we haven’t yet got to the green light”

“It is incredibly frustrating because (as you know) trade finance paper was included in a similar scheme in 2008/9 and it would work again.”

“I don’t want to put you to the trouble of a long email chain when ultimately this is an HMT call (and we continue to talk to them at every level) but could I ask you to do a one to one call with Lex Greensill so that he can brief you on where we have got to. This comes with all good wishes.”