Network Rail’s chief negotiator says that a deal to stop strikes is “in touching distance” as commuters face fresh travel disruption this week.
Tim Shoveller suggested that better communication of the deal would win over union members but hinted that the latest pay offer would not be improved.
Downing Street has also hinted a solution could be imminent after a source revealed to the Guardian that fresh talks are expected this week.
The source said that while issues remain, the rail dispute is viewed as the public sector dispute most likely to be resolved first.
Thousands of drivers and staff began the first of five consecutive days of rail strikes in ongoing disputes over pay, jobs and conditions.
About 40,000 members of the Rail, Maritime and Transport (RMT) union at Network Rail and 14 train operators are staging a 48-hour walkout, while drivers in the Aslef union will strike on Thursday in a separate dispute, in which the RMT is negotiating with the Rail Delivery Group.
Another 48-hour strike by the RMT is set to begin on Friday through to Saturday.
The RMT rejected Network Rail’s latest offer of a 5% pay rise this year and 4% in 2023 – with a guarantee of no compulsory redundancies before 2025 along with a discount scheme for families of rail workers was proposed.
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63.6% of members (of an 83% turnout) rejected the offer.
Shoveller said the network “only need 2,000 people who voted no last time to change their vote and the deal will pass”.
“We think that’s within touching distance,” he told BBC Radio 4’s Today programme.
“Some members are coming back to work, and we are seeing increasing numbers come back to work, but that’s not the way to resolve the problem or the dispute.
“The way to resolve that dispute is through an agreement and what we’re saying to the RMT is that it’s very clear from the referendum that they held, they did it very quickly, it was only open for a few days, that actually that was rushed, and it didn’t allow and give time for people to ask genuine questions there are associated with the reform elements of this deal,” he added.
“So, what we’re saying to the RMT is that we know which areas had been misunderstood by some of our staff, their members, and we want to make sure that we can work with the RMT now to make clarifications where there’s been misunderstanding and put the deal out again.”
Earlier, the RMT’s general secretary Mick Lynch has warned that industrial action will need to continue beyond May unless a reasonable offer is made.
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Speaking from a picket line at Euston station in London, he said: “They (the strikes) are likely to go ahead if there’s no offer that we can work on,” according to the Times.
“We would like to get into a situation where we’re negotiating constantly with the companies and where we didn’t have to have strike action, and then work up a settlement that our members could vote on and accept.
“But if we don’t get that there will have to be more action, and we’ve got a mandate that runs through to May this year, and if we have to go further, that’s what we’ll need to do. We don’t want that, though."
He added: “Our members are taking action right across the country, from the north of Scotland to the tip of Cornwall. The railway service has ground to a halt and it will be severely disrupted this week - we don’t take any pleasure in that."