Labour has formally called for the chancellor, Rishi Sunak, to publish all records of text messages, calls or other informal meetings connected to tax rules and Covid support schemes, following the row about lobbying by business interests. The demand came as Bernard Jenkin, the Conservative MP who chairs the powerful Commons liaison committee, said there should be tougher rules on conflicts of interest in government after text exchanges between Boris Johnson and the billionaire businessman James Dyson. Concern over lobbying has also centred on David Cameron’s repeated attempts during the start of the coronavirus crisis last year to seek official assistance for Greensill Capital, the finance firm for which the former prime minister was an adviser and had share options. Newly released exchanges, published by the Bank of England and Treasury on Thursday, show Cameron became increasingly desperate in tone, at one point complaining: “I must be missing something here.” Messages released previously show Cameron had repeatedly contacted Sunak and other Treasury ministers to seek full access to government Covid loan schemes for Greensill Capital, which has now collapsed. After Johnson promised to release details of relevant private lobbying communications, Anneliese Dodds, the shadow chancellor, has written to Sunak requesting he does the same, saying this would “restore public trust that your decisions and those of HM Treasury were taken exclusively in the public interest”. Dodds said: “We now know that his officials were fully aware that Greensill Capital was in financial trouble months before the government opened the door for it to lend hundreds of millions of pounds of taxpayer-backed loans. “But we don’t know what the chancellor told David Cameron he ‘pushed his team’ to do a day before Greensill’s affiliation to a Covid loan scheme was discussed at the Treasury, or what role he played in dishing out tax breaks by text to Sir James Dyson.” Asked earlier about the lobbying controversy, Jenkin said ministers should not be “locked away in ivory towers” with people unable to contact them. “The government is now under intense scrutiny – every meeting, every conversation that ministers have had with their officials,” Jenkin told BBC Radio 4’s Today programme. “What’s got to come out of this is obviously a system of managing conflicts of interest, which commands more public confidence and is more rigorous, but also a balance, there has to be a balance.” He said the appointment of an adviser on ministerial interests, a post which has been empty since November, when Sir Alex Allan resigned, was “pretty imminent”. Jenkin’s comments came after it emerged that the Cabinet Office is to launch an internal investigation into the leak of Johnson’s text messages to Dyson – with reports saying that some in No 10 are accusing the prime minister’s former adviser Dominic Cummings of being the source. The prime minister’s spokesperson said the decision had been made to launch a formal investigation into the leak, which showed that Johnson promised to change tax rules by saying: “I will fix it tomo!” The move came amid growing concern over Johnson’s use of a personal mobile phone in government. In another interview, the culture minister, Caroline Dinenage, told Times Radio ministers did not hand out their mobile numbers “willy-nilly” but those in government were required to engage with businesses, charities and unions all the time. “We engage with charities all the time, we engage with unions all the time,” she said. “The key thing is that we follow the process, we pass anything like that on to the civil service team to take forward. There are very clear rules and that’s what we all do.” Jenkin, meanwhile, defended his decision to reject calls by Labour to launch an investigation into Johnson’s conduct, insisting that the liaison committee did not have the remit to carry out its own inquiries.