The government is facing growing anger over its refusal to join last-ditch talks to avert the biggest rail strike for three decades, with millions of people facing a week of cancelled trains and union leaders saying industrial action could spread. With 40,000 rail workers due to join three daylong walkouts this week, Grant Shapps, the transport secretary, insisted it was not the government’s job to negotiate with the unions over pay, conditions, job cuts and safety. But Jake Berry, a Conservative MP and former rail minister, was among those who said ministers should get around the table with Network Rail – which is government-owned – train operators and the unions. Labour demanded ministers drop the boycott of talks, which continued on Sunday in a bid to bring the threatened action to a halt. The strike is due to start on Tuesday, followed by further strike days on Thursday and Saturday, with RMT union members walking out. Because of knock-on disruption, a special timetable will be in operation from Monday, with some evening services curbed, until Sunday. About 20% of trains will run on mainlines and urban areas. The RMT and Unite are also holding a separate 24-hour walkout for London Underground workers on Tuesday, which will cause huge disruption to the tube. There have been numerous warnings from union leaders in recent weeks about the prospect of further industrial action this year because pay deals are falling way short of soaring inflation at more than 10%. Care workers, civil servants, teachers and refuse collectors are among those that may ballot for strikes in the months ahead. Mick Lynch, the general secretary of the RMT, also raised the prospect of a rolling programme of train strikes if there is no resolution to the dispute. He told Sky News: “If there is not a settlement, we will continue our campaign.” He said: “I think there are going to be many unions that are balloting across the country because people can’t take it any more. We’ve got people doing full-time jobs who are having to take state benefits and use food banks. That is a national disgrace.” On Sunday night, a rail industry source said there was a “sliver of hope” of a resolution, with talks between the rail industry and unions continuing into the evening after starting at 2pm. Nevertheless, the two sides still appeared far apart on many of the main issues. The strikes also involve rail cleaners, customer service assistants and ticket office staff, who all earn much less than the average rail worker salary and stand to lose the greatest proportion of their income in real-terms wage cuts. Louise Haigh, the shadow transport secretary, wrote to Shapps on Sunday night to say: “The only way to sort this out is for your government to stop boycotting the talks and get around the table. “Patients, schoolchildren, low-paid workers and passengers need a resolution – and they will not forgive the government if they do not lift a finger to resolve this.” Keir Starmer accused Shapps of wanting the strikes to go ahead in order to sow division – an allegation the transport secretary dismissed as “crazy”. Speaking to a local government conference on Sunday, the Labour leader said: “They want the country to grind to a halt so they can feed off the division. Instead of spending their time this week around the negotiating table, they are designing attack ads. “Instead of grown-up conversations to take the heat out of the situation, they are pouring petrol on the fire. Instead of bringing people together in the national interest, they are stoking division in their political interest.” But Shapps insisted the RMT union’s request for a meeting was a “stunt” and the union was “determined to go on strike”. “In what sort of crazy world would anyone want to see our transport sector grind to a halt?” he said, highlighting students unable to attend exams and people likely to miss hospital appointments and struggling to get to work. He told the BBC that the RMT was “nostalgic for the power of the unions in the 1970s when they used to go and have sandwiches in No 10 – we’re not going back to those days”. The Conservatives have consistently attempted to associate the union-backed Labour party with the strikes, although Starmer has repeatedly stressed that he thinks the walkouts should not happen. The planned strikes will mean six days of disruption, with trains limited to one an hour between 7.30am and 6.30pm on major intercity and urban routes. Services will start later and be reduced on subsequent days. The action is being taken by Network Rail employees and onboard and station staff working for 13 train operators in England. The RMT has said thousands of jobs are at risk in maintenance roles and that ticket office closures are planned on top of pay freezes during a time of high inflation. The Sunday Times reported this weekend that there are plans to close all ticket offices by September in a bid to save £500m. The walkout by signallers will have most impact, particularly in more rural areas – leading to line closures in places including in Wales where there is no direct dispute with the train operator. Most operators have told passengers to only travel if necessary on strike days. Northern Rail has advised passengers not to attempt to travel for the whole week.