The Co-operative Bank is trying to reassure its customers that it would not need a multimillion-pound taxpayer bailout after its debt was downgraded to junk status and its chief executive suddenly quit.

The move by the ratings agency Moody's to take the axe to the Manchester-based bank's credit rating followed weeks of speculation about its financial position after it posted £600m losses in March and then pulled out of a deal to buy 632 branches from Lloyds Banking Group.

Moody's warned that the bank might need "external support" – perhaps from its parent group which owns grocers, pharmacies and funeral homes – if it could not bolster its financial position. The agency cited concerns about the Co-operative incurring more losses from loans to property companies and the slow integration of the Britannia Building Society, which the Co-operative took over three years ago.

The City was stunned by the scale of the downgrade – six notches – which will raise the price at which the bank borrows on the financial markets and illustrates the speed at which the agency believes the bank's finances have deteriorated.

While the Co-operative admitted it needed to raise fresh capital, it took to Twitter to insist that it could plug any shortfall through actions it already had in train to sell off its insurance business and scale back part of its bank. "In light of today's news, we would like to reassure customers and members that we haven't sought nor do we need government support," the Co-operative tweeted. The Co-op stressed that it had plenty of liquidity.

The bank has 6.5 million customers and a reputation for customer service and an ethical stance. It has a 1.5% share of the current account market and had been regarded by the government as key challenger in the high street to the big four players, Lloyds, Royal Bank of Scotland, HSBC and Barclays.

Amid suggestions that Co-operative might decide to pull out of banking altogether, it insisted it would continue to offer banking services even though it is now without a permanent boss after Barry Tootell resigned. Until a successor is found, insider Rod Bulmer will take on the head role at one of the most challenging periods in the bank's history.

The action by Moody's caused concern in the trade union movement at a time when the heads of Britain's biggest unions were attending the annual general meeting of the union-backed Unity Trust Bank, which is 26.7% owned by the Co-operative.

Billy Hayes, general secretary of the Communication Workers Union (CWU) and a non-executive director of the Unity Trust Bank, said the Co-operative's downgrade was a "major worry for the unions and our members".

Hayes said the unions might call for a public inquiry into what has gone wrong at the Co-operative Bank, where many union members have accounts, and may call for bonuses paid to executives to be clawed back.

Richard Wilcox, managing director at Unity Trust Bank, said that while the Co-operative had been discussed at Unity's scheduled board and annual meeting, "the relationship with Co-op continues to be managed as normal. We work as an independent entity and are not impacted by changes to the credit rating of the Co-operative Bank."

The Co-operative said it was disappointed about the downgrade from A3 to Ba3 and did not provide any details about any payoff for Tootell, who had been leading the planned takeover of the Lloyds branches. He had replaced Neville Richardson, the former boss of Britannia who was appointed to run the enlarged financial services business after the 2009 merger. Richardson left earlier than expected in 2011 with a final pay cheque of £4.6m.

The Co-operative's admission that it need to raise capital comes amid an industry-wide review of banking strength by City regulators, led by the new Prudential Regulation Authority, which identified a £25bn capital shortfall.

Individual banks are yet to be told precisely what their portion of this shortfall is but City sources believe the Co-operative could need between £800m and £1bn – a gap that it said it could fill by selling its general insurance arm, selling its life insurance concerns to Royal London and simplifying the bank.

"We do acknowledge like the rest of our banking sector peers, the need to strengthen our capital position in light of the broader economic downturn and the pending introduction of enhanced regulatory requirements and we have a clear plan to drive this forward throughout the coming months," a spokesman said.

Moody's questioned whether the bank's proposed disposals and scaling back of its businesses would be enough to bolster the bank's closely-watched capital ratio, which at 8.8% is low relative to its peers. The ratings agency said the Co-operative was unlikely to be able to generate enough extra capital from profits and that there was "material uncertainty" over whether the disposal programme underway would be enough.