Trade union opposition to the government's austerity programme will be stepped up this week as two of Britain's most powerful private and public sector unions prepare to deepen their alliance, while the TUC will confirm a huge protest march will be held in London on 20 October.

The Public and Commercial Services union, the largest civil service union in Britain, has been the subject of merger speculation with its much bigger counterpart, Unite, which has a predominantly private sector membership base and is the largest union in Britain with 1.5 million members. PCS delegates will vote on a motion at the union's annual conference this week to "explore" how to develop a co-operation agreement with Unite, although a merger will not be on the agenda.

Mark Serwotka, the PCS general secretary, said: "We want to get closer and closer to Unite, with the test being does it make for more effective trade unionism. And if it does, that's when the question of a formal merger will arise."

Serwotka said the trade union movement had to combat government spending cuts by combining public and private sector members. The majority of Unite's members are private sector employees, including branches at major companies from British Airways to Unilever, Vauxhall and Rolls-Royce. PCS has members at a range of government departments including the DVLA and UK Border Agency.

"We have got to look at the future of the labour movement and being more effective in fighting against government cuts. Closer co-operation with public and private sector unions will create the ability to fight back more effectively," Serwotka said.

Noting that a co-operation agreement with Unite has produced "excellent results so far", the PCS motion states that "the further development of relations between the two unions should be explored". If delegates back the motion, PCS and Unite members will co-operate more closely at companies such as Fujitsu and Cap Gemini, firms which carry out public sector work and have PCS and Unite representation.

The two unions are also working on a fourth national walkout in the protest against public sector pension reforms. A date of 28 June has been mooted but it is now thought that a one-day strike earlier in June or in early July is more likely.

The government claimed 150,000 state employees took part in the latest one-day strike, on 10 May though it was augmented by a police protest featuring more than 30,000 officers and surprise action by prison officers.

The TUC – which represents 58 unions with a total of more than 6 million members – is to confirm a successor to the "March for the Alternative" that was attended by up to 500,000 people on 26 March last year.

The protest will end with a rally in Hyde Park, London. The TUC said the march would reflect a "clear shift" against austerity in public opinion across Europe, after the French election result, Greece's political struggles and confirmation that Britain has entered a double-dip recession. "There is a sense in the trade union movement that the argument is turning quite strongly against the government's economic strategy," it said. "The march last year was about cuts to services and the impact of government policies. This will be a much broader critique of government and the fact that their policies are holding back growth, increasing unemployment and going against the grain of where things are moving internationally."