Ministers cannot allow unions to win the battle for higher pay as it would fuel a “vicious cycle” of inflation hurting the poorest, Deputy Prime Minister Dominic Raab said.

Mr Raab told Sky News’s Kay Burley that latest official inflation figures showing the increase in the cost of living hitting a new four-decade high of 9.1% illustrated why public sector pay restraint was needed.

He indicated that the publicly-backed rail sector would continue to hold out against RMT demands for a 7% pay increase amid the biggest train strike in three decades and threats for wider industrial action across the economy and public sector later this year.

Talks in the rail dispute collapsed earlier this week as an offer from employers of 2% plus a further 1% linked to modernisation reforms was rejected but it is now understood that a 4% offer, again linked to reforms, is on the table.

Mr Raab argued that big wage increases would help inflation stay higher for longer, eating into the value of incomes.

He said: “We really do understand the pressure that those on low incomes are facing at the moment, they’re struggling to make ends meet.

“We do need to have the the kind of pay restraint in the public sector that we have been talking about… otherwise we’ll just have the vicious cycle of inflation staying higher for longer.

“We can’t allow the unions in this very militant way that they have proceeded to win this argument because it will only hurt the poorest in our society.”

Mr Raab said the government was taking a “firm line” with unions to try to allay the “erosion of pay packets by inflation”.

He added: “At one level for the union I do understand, they feel their job is to protect their workers.”

But it would be “totally counterproductive” for the rail industry to agree to a 7% pay increase, he said.

Labour’s shadow culture secretary Lucy Powell accused Mr Raab of “goading” workers into strikes and claimed the Tories were “gleeful” about the dispute as they try to stoke division for political gain.

She told Sky News: “All the people who were so inconvenienced yesterday… put out of pocket, or who couldn’t go to work, will be rightly really angry that this government is actually pushing forward these strikes in order to save their own skin at the next election.”

Ms Powell was also pressed on the divisions that the strike has highlighted in her own party.

Asked about whether those Labour MPs in shadow ministerial positions who stood on picket lines despite an order from the party’s leader not to do so faced being sacked, Ms Powell said: “I’m sure these issues will be looked at.”