Britain's largest trade union, Unite, is launching cut-price memberships for students and the unemployed as it attempts to boost its ranks and counter David Cameron's "big society".

Unite will offer students, single parents and the jobless 50p per week "community memberships" as it focuses on neighbourhoods as well as workplaces. Trade unions are battling falling membership numbers and government spending cuts that will put their finances under further threat by eliminating public sector jobs – their most fertile recruiting ground.

In an interview with the Guardian, the general secretary of Unite, Len McCluskey, also warned that strikes by millions of state employees are "inevitable" this autumn because of government inflexibility over pension reforms, while he criticised Labour party leader Ed Miliband for an "ill-advised" attack on last month's public sector walkouts.

McCluskey said the trade union movement already reflects through its voluntary membership structure the Conservative party's "big society" vision of non-state organisations taking a bigger role in running public services. "David Cameron is talking about the big society. Well we are here. In many ways we are the big society. It will include students, single parent families, unemployed people, retired individuals. If they want to come join us in this large family where we can link our work places and families together, that's the type of union that we are looking to develop."

Unite is considering offering legal support and education facilities under the community membership scheme in exchange for "collective community action", which could include supporting industrial action or campaigns against job cuts. Unite has around 1.4 million members but its former general secretary, Tony Woodley, has warned that the union movement's finances are being hit by falling membership. According to the Office for National Statistics, trade unions lost 179,000 members last year, leaving a total membership of 6.5 million.

McCluskey added that the TUC march against public sector cuts this year, attended by 250,000people, underlined the potential for a community membership project. "There are millions of people out there who are vulnerable and without a voice. As the March 26 demonstration showed, I will bet that there are tens of thousands of people who were not union members. The only organisations speaking up for people are trade unions. I want to extend our remit into areas where perhaps we have not represented people before. If advice bureaus close down where do people seek help?"

In a blunt assessment of Labour's record in power, McCluskey said the party's "absolute adherence to the financial markets and the slavish following of neo-liberalism" had created a poverty gap. Unite is Labour's largest donor and Miliband's decision to label the 30 June public sector strikes as "wrong" riled a trade union movement whose votes were crucial in electing the younger Miliband ahead of his older brother David. "I think Ed was wrong to condemn the strikes on 30 June," said McCluskey. "He was ill-advised to condemn those workers. We are talking about teachers here."

However, the Unite leader added that Miliband had "looked the part" last week after making the political running during the phone hacking scandal. "He is only a young man growing into the job and I thought his performance this week has been outstanding."

Despite its status as Britain's largest trade union, Unite has only 250,000 public sector workers on its books compared with more than 1 million at Unison. Nonetheless Unite is involved in talks with the government over reforms to public sector pensions and is pessimistic about the outcome.

"I think it is inevitable that there will be strikes in the late autumn, based on the government's intransigence at the moment," said McCluskey. As a negotiator I would always hope that they become more flexible in their negotiations."

The TUC is leading the talks under its general secretary, Brendan Barber, and McCluskey acknowledged that he faced a "difficult task" in corralling such a broad coalition, amid fears that traditional differences will soon come to the fore and reduce the likelihood of joint action. "The TUC is conducting the campaign of trying to resist the cuts and that's a difficult task for Brendan to co-ordinate. In doing that I have made it clear that we need to be more honest with each other."

McCluskey warned that other issues at the centre of the deficit reduction programme, such as NHS reform, could stoke a wave of disputes. "All these [changes] are deeply, deeply ideological and they not only threaten jobs but the social architecture that holds our nation together.

"I can see a constant rolling out of disputes, whether they be nationally coordinated or spasmodic from one locality to the next." Unite and Unison have already joined forces to co-ordinate a wave of strikes at Southampton city council in protest at the imposition of a pay cut of up to 5% on more than 4,000 staff.

Six months into his own leadership, McCluskey also expressed hope that the phone hacking scandal will give Miliband more confidence in the face of press criticism of his union links. "Ed is still worrying about the media attacking him for being in the unions' pockets. The reason why him and other leaders went out of their way to criticize the strikes was in response to the right wing media agenda. Hopefully after this week Ed will realize that he does not have to worry about the media and worry about re-connecting with people, including organized labour."