The minimum wage should be increased to £15 an hour as soon as possible to help millions of low-paid workers struggling amid the cost of living crisis, the TUC has said.

In a move that opens a fresh policy gap between unions and Keir Starmer’s Labour party, the TUC has thrown its weight behind calls for a more ambitious legal floor on pay rates. The union body said the government needed to draw up plans to get wages rising as workers suffer the biggest hit to living standards on record.

It said too many workers were living “wage packet to wage packet”, and a £15 minimum should be in place by at least 2030 but could be achieved sooner with a government that was serious about getting wages rising after years of sluggish pay growth.

The minimum wage is now set at £9.50 for those aged 23 and over, with lower rates for those who are younger.

Strike action has spread across the economy during a summer of unrest, as workers see the real value of their wages cut by inflation soaring to the highest level in 40 years.

Port workers at Felixstowe have been on picket lines this week demanding higher pay to compensate for inflation rising above 10%, with further increases expected within months driven by rising energy bills. Postal services will also be disrupted by four days of strikes at Royal Mail, starting on Friday.

Frances O’Grady, the general secretary of the TUC, said: “Millions of low-paid workers live wage packet to wage packet, struggling to get by – and they are now being pushed to the brink by eye-watering bills and soaring prices.

“For too long workers have been told that businesses can’t afford to pay them more. But again and again the evidence has shown that firms are still making profits and increasing jobs – we can afford higher wages.”

Britain already has one of the highest minimum wage levels compared with other advanced economies, ahead of Canada, the US and Spain, but behind Germany, the Netherlands and Luxembourg. The TUC said a £15 minimum wage by 2030 would place Britain above all its peers.

In a report setting out its plan, the TUC called on the government to work with the Low Pay Commission to reach the level “as soon as possible over time”.

Ministers need to put in place a target for the minimum wage to reach the equivalent of 75% of median pay, the TUC said, an upgrade on the current plan to hit two-thirds of median pay by 2024. Median wages are now £14.85 an hour.

However, business leaders are worried about rising costs and the prospect of a long recession caused by the cost of living crisis.

Matthew Percival, the CBI’s director of skills and inclusion, said: “Business supports a higher wage economy, but the only sustainable path – not only for those earning the minimum wage, but right across the economy – is higher productivity.”

The TUC said action was needed after years of weak pay growth under the Conservatives. It claims median pay levels would have been £3 an hour higher if pay growth had continued at the rates seen before the party came to power in 2010.

Calls for a £15 an hour minimum wage have been gathering pace among union activists after campaigns pushing for a $15 (£12.67) legal pay floor in the US. However, the TUC stance could risk adding to tensions within Labour, with the party reluctant to commit to a specific figure under Starmer’s leadership.

Labour set out its plans to link the minimum wage to living costs in a joint article in the Guardian by Angela Rayner, the deputy leader, and Rachel Reeves, the shadow chancellor last week. It has not however said how much it could rise to under its proposals.

The TUC’s intervention comes almost a year after the shadow employment secretary Andy McDonald quit the opposition frontbench in protest at Labour’s failure to support £15-an-hour.

Speaking to the Guardian, McDonald said the timing, before next month’s Labour party conference in Liverpool, was unsurprising. “Of course I resigned 12 months ago over the very issue, because in my view £15 ought to have been nailed-on as the standard.

“The turn of events over the last several months have made it even more important that workers get a fairer share of the wealth they create. The fundamental thing is that everyone needs a wage they can live on. Right now, it’s a pipe dream for too many people.”

A government spokesperson said it was helping families with rising costs, adding: “We are determined to make work pay, and this year’s increase is the largest ever ‘national living wage’ rise, helping millions of families across the country.”