Conservative MPs have been accused of blocking a parliamentary committee’s attempt to scrutinise the former HSBC boss and minister Stephen Green over the tax scandal at Britain’s largest bank.

A proposal put forward by a Labour MP to call the bank’s former chief executive, who later became a Conservative minister, before the powerful Tory-dominated public accounts committee (PAC) has been rejected, sources confirmed.

Lord Green, who left HSBC to join the House of Lords as a Conservative peer and trade minister in 2010 after three decades at the bank, has yet to be questioned by any parliamentary committee over the scandal. Green stepped down as a trade minister at the end of 2013 but remains a peer.

The disclosure will prompt further accusations that the Conservatives have launched a concerted effort to stop scrutiny of Green because of his relationship with the prime minister.

Austin Mitchell, the MP for Grimsby, said he proposed that Green should be brought before the PAC, parliament’s tax and spending watchdog, in a preliminary hearing earlier this month.

But it soon became clear that Tory members of the committee were against his suggestion, he said. The committee is made up of eight Tory MPs, five Labour MPs and one Liberal Democrat.

Mitchell said: “The public has a right to know and parliament has a right to know, what the man in charge knew about this massive scandal. He needs to clear these things up. He has taken the glory and taken the money. To say that he did not know what was going on is ludicrous.”

The revelation of the failure to summon Green came after a stormy session of the PAC – including interrogation of HSBC’s current chief executive, Stuart Gulliver; the non-executive director Rona Fairhead, who is also chair of the BBC Trust; and Chris Meares, the former head of HSBC global private banking – in which:

• Margaret Hodge, the committee’s chair, said that Fairhead’s performance as an HSBC director, for which she is paid £513,000, meant that she was no longer fit to continue in her £110,000-a-year role heading the BBC Trust. “I really do think that you should consider your position and you should think about resigning, and if not, I think the government should sack you,” she told Fairhead.

• Stuart Gulliver, the chief executive, acknowledged that revelations about his personal tax and banking affairs – that he was a non-domicile with a Swiss bank account who at one point was paid via a Panamanian company – were further damaging the reputation of the bank.

A second parliamentary committee has also been prevented from summoning Green, according to a Labour MP. John Mann, who sits on the Treasury select committee, said attempts to call the former minister had been blocked by Tory members. “The Tories won’t allow [Green] to be called. They are trying to palm this off until after the election,” he said.

A spokesman for the Treasury committee said no formal proposal to call Green had been put to it. “We were considering who to call in our session a couple of weeks ago and it was decided we wanted to respond to HSBC as it stood now, a forward-looking approach. These allegations raise some important questions but we decided to focus on the current management and there were some strong questions during the session,” he said.

Green was the chief executive and then chairman of HSBC from 2003 and 2010. The Swiss arm of the bank has been accused of enabling clients’ tax evasion.

The Geneva subsidiary, which routinely allowed clients to withdraw “bricks” of cash, held accounts for drug dealers and colluded with wealthy clients to conceal undeclared “black accounts”, was created while Green was in charge.

Green is an ordained minister of the Church of England and left HSBC with a £19m pension pot. He joined the board in 1998, when he was given responsibility for overseeing private banking and other operations.

One of the main objections to Green’s attendance before the PAC came from Tory MPs who said they were concerned over the protocol of questioning a member of the House of Lords. But other peers have been scrutinised by parliamentary committees before, including Lord Patten, who was questioned by the culture, media and sport committee, one Labour MP said.

Chris Heaton-Harris, a Conservative member of the PAC who attended the preliminary hearing, confirmed that he was content with the decision not to invite Green. “The committee came to an agreement which I was happy with,” he said.

Hodge, the PAC’s chair, told Channel 4 News that the decision not to invite Green was “the committee’s decision”.