Grant Shapps has urged the head of the Rail, Maritime and Transport (RMT) union to put Network Rail’s pay offer to workers for a vote as strike chaos continues.

In a letter to RMT general secretary Mick Lynch on Saturday afternoon, the Transport Secretary said the railway operator’s proposal of an 8% pay rise over two years is “fair” and members should have the opportunity to resolve the dispute.

He also called on the union to accept proposed reforms to modernise the railway sector.

It comes as members of RMT, the Transport Salaried Staffs’ Association (TSSA) and Unite walked out for 24 hours on Saturday, affecting Network Rail and several train companies across the country.

The action is the latest in a series of walkouts over the last few months amid a stalemate between unions and train operators, which has caused travel chaos across the UK.

Mr Lynch has rejected suggestions that rail workers would agree to the offer on the table if the union put it to a vote.

But Mr Shapps made a fresh appeal on Saturday before criticising the union for how the industrial action is affecting the public.

In his letter shared on Twitter, the Transport Secretary wrote: “Network Rail has tabled a fair, legitimate pay offer (8% over two years).

“It is only right that you now put that offer to your members and call off the strikes whilst you do so.”

Mr Shapps cited some TSSA members recently voting in favour of the deal before accusing other unions of pressurising other TSSA members into cancelling another vote.

“It is in no one’s interest to take away members’ opportunity to resolve disputes,” he said.

Mr Shapps described the union action as a “kick in the teeth” to workers who cannot travel to their own jobs.

He wrote: “Whilst the rise of home working has limited your ability to bring the country to a standstill, your action is disproportionately impacting those who have no option but to travel to work.

“Consider the hospital porter, cleaner and everyone else who needs to physically be at their place of work. Your action is often harming the least well paid the most.”

The Transport Secretary said employers have a pay rise on the table for RMT members but it will not be put forward until the union agrees to reforms that “will bring the railways off taxpayer-funded life support”.

He said: “The longer the RMT continue to call further strikes whilst refusing to agree to these reforms and refusing to even put offers to its members, the more long-lasting damage is being done to the very sector from which your members draw their livelihoods, and on which key workers rely.”

Our members are not going to be bribed, the offer is puny and they’re not ready to accept it

The two sides are as far apart as ever in resolving the row despite months of talks.

Mr Lynch rejected Mr Shapps’ suggestion that RMT members would agree to the current offer if it was put to a vote, as he spoke to broadcasters on Saturday morning.

Asked on BBC Breakfast whether he had evidence of this, Mr Lynch said: “Absolutely, I did a meeting on Wednesday evening, the night before the strike of 14,000 RMT members, in an online rally and our members are out today demonstrating.

“I speak to thousands of our members every week, we consult at least 600 Network Rail reps on a weekly basis and we know exactly what the mood of our members is.”

Mr Lynch also claimed that members of the smaller TSSA union, who voted to accept a pay deal, “have been bribed to break this strike”.

He said: “Our members are not going to be bribed, the offer is puny and they’re not ready to accept it.”

Mr Lynch claimed public support for the dispute is “entrenching”.

“There are campaigns and rallies being launched right across the country in support of these type of activities,” he said.

“I think the British public are fed up of being ripped off by this Government and by corporate Britain, which have seen companies like BP and British Gas making massive profits while people are struggling to make a living.

“The companies are being supported in this by the Government and we’re determined to get a square deal for our people and that’s exactly what we’ll achieve and the public seems to be right behind us in that campaign.”