Mark Serwotka, the general secretary of the Public and Commercial Services Union (PCS), said a coordinated mass walkout could cause “chaos” and succeed in driving the Conservatives out of government.
Speaking in Liverpool at a fringe event of Left-wing MPs, Mr Serwotka said industrial action by civil servants – who his union represents – would lead to cancelled driving tests, huge border queues and problems collecting taxes.
“We are balloting for sustained action in targeted areas, and I’m going to say it, to cause chaos, to put pressure on the government,” Mr Serwokta told the room to a standing ovation.
“When we win the ballot the action we will take will be hard-hitting but we believe people will support us because we believe people know that for every union that wins, we all win.
“If any union is planning a one or a two-day national strike, we pledge that we will join them. And if we get millions of people on strike at the same time, hundreds of thousands taking action, that demonstrates our worth.”
Labour MPs at the rally included former John McDonnell, Rebecca Long-Bailey and Richard Burgon, former members of Jeremy Corbyn’s shadow cabinet.
Mick Lynch, the general secretary of the Rail and Maritime Union (RMT), was also in attendance.
Earlier on Sunday, he told the BBC: “If people can’t take lawful industrial action, they’ll have to take unlawful industrial action.”
And at a separate fringe event, he urged Sir Keir Starmer to place nationalisation at “the heart of” the party, adding: “Public ownership is good… It should be a permanent value that we hold in regard to everything.”
During her opening speech in the main hall on Sunday, deputy leader Angela Rayner said: “Conference, so long as I have a breath left in my body I will defend [our] rights, including the right to strike.
“And when in power we will repeal all the anti-worker and anti-trade union laws this Conservative government has enacted. All of it.”
But speaking to the BBC’s Sunday with Laura Kuenssberg programme, Sir Keir said the “single most important thing” he could do for striking workers was to “usher in a Labour government”.
Kwasi Kwarteng, the Chancellor, last week announced new legislation that will force unions to put pay offers to a member vote – ensuring strikes can only be called after negotiations have “genuinely” broken down.
The Government also plans to press ahead with minimum service levels, similar to those in other European countries, that would stop unions from closing down transport networks during industrial action.