Britain's banks will be urged by the Treasury to take multimillion pound losses as part of Europe-wide plans to prevent a catastrophic meltdown of the Greek financial system.

Despite the assurance of David Cameron that the UK taxpayer will not pay towards the latest EU bailout of Greece, Treasury officials are working behind the scenes to persuade British banks holding Greek bonds to take a "haircut" now as the best way to avert a potential global crisis. Britain's banks hold about £2.5bn of Greek bonds.

One idea, proposed by Germany, is that the banks would be persuaded to swap Greek bonds for loans on less favourable terms when they expire – a so-called "soft restructuring" that would help ease the pain for Athens.

Politicians across the EU are battling to secure "private sector involvement" in the Greek rescue alongside government and IMF help in the hope of preventing Athens from defaulting on its debts, a move they fear could start a ripple effect in world markets.

Analysts say even a debt swap, under which Athens would pay its debts over a longer period, would leave bondholders facing a reduction in the value of their investment. But officials argue that only if private banks take a hit now can the damage be limited.

The Treasury so far has been on the sidelines of EU discussions about how to ensure private sector creditors play their part, partly because of Cameron's insistence that UK taxpayers will not help to finance a second Greek bailout.

The prime minister's refusal to put money into the latest rescue led to criticism of the UK's stance behind the scenes at a summit in Brussels last week. Senior European figures said London needed to focus more urgently on the potential effect of a Greek default on the UK's banking sector and economy.

"The UK has the third largest exposure after France and Germany," said a high-level EU source. "It should be aware of the effect of standing aside from discussions."

But Whitehall insiders have confirmed that chancellor George Osborne's staff are on the case, working on ways to involve British bondholders in rescue moves that will almost certainly involve a short-term hit.

Another worry is that Britain's banks and hedge funds have written multibillion-pound insurance contracts – credit default swaps – that would be triggered if Greece defaults.

Erik Britton, director of City consultancy Fathom, said: "It's not the direct exposure, it's the indirect exposure and the implications of an unruly default that I would be worried about. French and German banks bought Greek bonds, and they took out insurance against default. Who did they take out that insurance with? The US and UK banks. There has to be a loser – who's the loser?"

A fresh bailout for Greece will go ahead on condition that its parliament votes for new austerity and reform programmes. It is expected to total about €110bn, with about €30bn coming from bondholders, €30bn from privatisations and the rest from eurozone members and the IMF.

Persuading the private sector to play a part is seen as crucial to the chances of averting a Greek disaster and was a key part of German chancellor Angela Merkel's pitch in Brussels. Without this, EU leaders fear Greece will default, triggering payouts on a web of complex financial insurance products and creating chaos in world markets as investors struggle to work out who owes what. Some analysts fear default could create a "Lehman moment", like the aftermath of the collapse of the giant US investment bank in 2008, when investors lost confidence in each other and the world financial system froze up.

At the inaugural press conference for the Bank of England's new financial policy committee, governor Sir Mervyn King described the deteriorating situation in the eurozone as a "mess" and warned that, although Britain's banks own a relatively small number of Greek bonds – about £3bn worth – there could be dramatic knock-on effects if a default resulted in a loss of confidence throughout the global financial system.

That gives Treasury officials a strong incentive to ensure that the banks sign up. Without a voluntary agreement from investors, the powerful credit ratings agencies will declare that Greece has defaulted, spreading chaos. US Federal Reserve governor Ben Bernanke last week urged European governments to resolve the Greek crisis or risk threatening "the European financial system, global financial system, and European political unity".