Talks are not due to resume until next week, with Mr Harper saying they could not begin until the RMT’s two 48-hour walkouts, on Tuesday and Wednesday, and on Friday and Saturday, had concluded.
But Mr Lynch, speaking from the RMT picket line outside Euston station, told Sky News: “I would go and meet him now if he wants, or he can come here and meet me, and we can hammer things out. I will meet him at 10am if he wants.”
There were widespread closures across the rail network on Tuesday, including no Elizabeth line trains between Paddington and Heathrow and between Liverpool Street and Shenfield – though the line, the busiest rail route in the country, was operating between Paddington and Abbey Wood.
The London Overground suffered part-closures after services started late. Last trains were due to depart by 6.30pm. The Tube was running but there were knock-on impacts on some sections shared with Network Rail, such as the northern end of the Bakerloo line.
Network Rail advised passengers to only travel if absolutely necessary for the rest of the week. It said some trains would run but those that did were likely to be overcrowded, with the risk of passengers being unable to board.
South Western Railway said some routes were closed and trains would stop running at 630pm. Southeastern said its last trains from London Bridge would depart before 6pm, with the last Sevenoaks train leaving at 5.16pm.
There has been no face-to-face meeting with the Government since December 15, when the RMT met rail minister Huw Merriman.
Mr Lynch said ministers had “torpedoed” any chance of resolving the dispute by inserting a clause at the last minute requiring the union to accept the principle of driver-only trains across the rail network.
Mr Harper said a “new and improved offer” from Network Rail had been accepted by two other unions – the TSSA and Unite – and urged the RMT to compromise.
But he admitted the deal on offer, of four per cent one year and five the next, with extra payments for lower paid staff, was not above the current rate of inflation.
“We have not got the money to give inflation-busting pay rises to everybody,” he told Good Morning Britain.
He said a third of RMT members at Network Rail had voted to accept the deal, describing the union’s latest series of walkouts as “deeply unhelpful”.
Mr Harper said: “I think in the New Year it’s time for the RMT to get off the picket line, back round the negotiating table and ministers will do what we can to facilitate them coming to a deal with the employers.
“I want to get these rail disputes sorted out for the benefit of the travelling public. There is a fair and reasonable offer on the table.”
Network Rail said some RMT members had returned to work, despite union orders to go on strike. Chief negotiator Tim Shoveller said some staff had “misunderstood” the terms of the deal and called on the RMT to put it to its members again. He said if 2,000 members who voted no in an electronic referendum last month changed their vote then the deal would pass.
However the RMT remains in dispute with 14 train operating companies, with no sign of a deal – primarily due to the Government wish to remove guards from trains, and what the RMT believes are plans to close all ticket offices and reduce track maintenance schedules.
Passengers on the West Coast Main Line face further problems this week. A landslip at Carstairs has forced the closure of the between Carlisle and Glasgow until at least Friday. Avanti West Coast advised passengers not to travel to and from Scotland. The East Coast Main Line between King’s Cross and Scotland remains open.