Employees should consider using strike action to disrupt the Olympics as part of their campaign against the government's spending cuts, the leader of Britain's biggest union has declared.

In an interview with the Guardian, Len McCluskey, the leader of Unite, said attacks on public sector workers were "so deep and ideological" that targeting the Games would be justified. The call came as the RMT union increased the pressure on the capital's mayor, Boris Johnson, over delivering a strike-free event by declaring a formal dispute after rejecting an Olympics pay deal for London Underground staff.

"If the Olympics provide us with an opportunity, then that's exactly one that we should be looking at," said McCluskey. He also said that any attempt by ministers to tighten anti-strike legislation would lead to unions deliberately breaking the law. Government plans to cut the value of public sector pensions prompted the biggest strike for three decades in November last year. Although some unions have scaled back their opposition to the proposals, McCluskey said industrial action would "drag on and on" and that it would involve "all forms of different protest and action".

That included possibly hitting the Olympics, he said: "The attacks that are being launched on public sector workers at the moment are so deep and ideological that the idea the world should arrive in London and have these wonderful Olympic Games as though everything is nice and rosy in the garden is unthinkable.

"Our very way of life is being attacked. By then this crazy health and social care bill may have been passed, so we are looking at the privatisation of our National Health Service. I believe the unions, and the general community, have got every right to be out protesting."

McCluskey was speaking in general terms and he admitted Unite did not at this stage have specific plans for action during the Olympics. But he said his union represented London's 28,000 bus drivers and staff, who are involved in their own row about extra payments during the Olympics. The bus workers want £500 in supplementary pay for the Games, in line with deals at Network Rail, Virgin Trains and London Overground. "They will be examining what leverage points we have, and the Olympics will clearly come into play," he said.

McCluskey said that, because of the seriousness of the issues at stake, he was encouraging the public to engage in "all forms of civil disobedience within the law" in the campaign against cuts.

"Our parents and our grandparents, having defeated fascism in Europe, came back determined to build a land fit for heroes. They gave us the welfare state, the National Health Service, universal education. All of that is being attacked," he said. "I, for one, am not prepared to stand by and have my children or grandchildren say to me, what did you do when this was being taken away from us?"

The Olympics were a focal point, he said. "If there is a protest, then the purpose of protest is to bring your grievances to the attention of as many people as possible."

Britain's largest rail union escalated its dispute with Transport for London (TfL) on Tuesday. It declared a formal dispute over Olympics pay for tube staff and announced a ballot of administrative staff at TfL over the right to take leave during the Games.

It is the underground dispute that threatens to cause Johnson the biggest problem. The RMT represents about 10,000 of the tube's 18,000 staff, from drivers to platform staff, and any industrial action during the Games would be highly disruptive.

A spokesman for the RMT stressed the union wanted a settlement despite turning down an offer last month of £500, including £100 for meeting customer satisfaction targets and an extra £20 a shift.

"The formal move to declare a trade dispute gives us scope to declare a ballot [for industrial action] if we choose. We want to get this settled," said the RMT spokesman.

On Thursday underground bosses and the RMT are due to hold talks at the conciliation service Acas, raising hopes of a deal.

The next strike over public sector pensions is expected on 28 March, with Unite's health workers, civil servants in the Public and Commercial Services union and the National Union of Teachers contemplating combined action. More than one million public sector workers took part in the national walkout on 30 November but numbers could be lower next month because the largest public sector union, Unison, is focusing on settlement talks.

The PCS has mooted rolling programmes of action by specific groups of workers, such as call centre staff, or work-to-rule campaigns in which employees carry out no more work than the bare minimum stipulated in their contracts.

Last week a meeting of the British Medical Association, the union representing 130,000 doctors and medical students, decided to ballot for industrial action short of a strike over NHS pension reforms after eight out of 10 members rejected the changes.

Some Conservatives have already been arguing that the government should tighten the strike laws in response to what they perceive as militant unionism represented by leaders such as McCluskey and his ally, the PCS general secretary, Mark Serwotka.

One idea, backed by Johnson and not wholly ruled out by ministers, is for unions to be prohibited from striking unless 50% of their members back strike action – not just 50% of those voting. In his interview McCluskey signalled that unions would refuse to comply with such a law, even if that meant calling strikes illegally. "If [ministers] make these attacks against us, trying to limit the type of strike action … if they push us outside the law, they are going to have to live with the consequences of that," he said. "Because if we need to break the law in order to defend what are our basic human rights – right of association – then we will do that."

McCluskey also used the interview to say that Ed Miliband and Ed Balls should "worry less" about fiscal credibility.

Instead of trying to impress "the chattering classes" by embracing the case for austerity, McCluskey said the Labour leader and his shadow chancellor should concentrate on winning credibility with voters by proposing alternatives to "the fear and the misery and the gloom and the despair" represented by the coalition.