Tens of thousands of commuters faced lengthy delays as 40 per cent of services were cancelled, while others were severely reduced. Many travellers took to the roads, causing heavy congestion on a day when driving conditions were already poor because of heavy rain.

The signal workers, employed by Network Rail, walked out at midday in the first of two 24-hour stoppages, with the second scheduled for noon tomorrow. About 450 members of the National Union of Rail, Maritime and Transport Workers (RMT) are involved in the dispute over staff rosters. The union has accused Network Rail of wanting to make changes to rosters at short notice, but the company denies the claim.

Although the industrial action was expected to disrupt services for four days, RMT officials and Network Rail agreed to get back round the table today, raising hopes of a resolution. The discussions, helped by Acas, the conciliation service, are scheduled to take place at Network Rail's head office in Glasgow at 2pm, shortly after the first walk-out finishes.

Alex Salmond, the Scottish First Minister, hailed the meeting as a positive step forward, and urged the two sides to come to a resolution.

“It must be a good sign that both sides are willing to resume talks and I welcome this development,” he said.

“It is deeply unfortunate that one remaining issue in the dispute has resulted in substantial inconvenience to the travelling public today and tomorrow and both the union and management must do their utmost to resolve their differences and avoid a repetition of the action.”

Services wound down after the morning rush hour yesterday, affecting all main routes north of the Border. Only half the usual number of trains ran on the main commuter route between Edinburgh and Glasgow, with the last service at 6pm.

There were no trains operating north of Perth, as the larger number of small signal boxes made the area more difficult to cover with contingency staff, but replacement bus services have been running to Aberdeen and Inverness. Some cross-border routes were also affected when Virgin Trains cancelled a handful of its services last night and this morning.

The concourses at Central Station and Queen Street Station in Glasgow, two of the biggest in Scotland, were quiet yesterday as passengers sought to avoid the stoppages.

Travellers who had ventured out voiced anger yesterday over the strike. Jean Morrison, chief executive of SCAR, an Aberdeen-based fuel poverty charity, who had to attend a business meeting in Glasgow yesterday, said it had taken a day out of her working week.

An assistant in a catering outlet in Queen Street station pointed out that it was not only commuters who had been affected. “We are probably going to shut early tonight, which means we are losing five hours of trade and our wages could be cut.”

Despite the failure on Monday of talks aimed at averting the strike, both the union and railway management remain hopeful of reaching agreement today.

Ian Macintyre, RMT regional organiser for Scotland and Northern Ireland, who joined a picket line at Central Station yesterday, said: “We are happy that there are talks tomorrow but they have got to be meaningful.”

David Simpson, Network Rail route director for Scotland, said: “It is encouraging that the RMT has agreed to get around the table again but we call on them to suspend Thursday's strike while we try to find a resolution.”

Mary Grant, managing director of the train operator First ScotRail, called on the two sides to put passengers first. “Our customers are caught in the middle of a strike which has nothing to do with us,” she said.

“We will continue to run as many trains as possible, but there are limits to what can be provided.

“It is hoped Network Rail and their signallers will resolve issues and end the misery for our customers.”

Tavish Scott, leader of the Scottish Liberal Democrats, said that the SNP administration needed to work out what role it was taking in resolving the dispute: “First they said it was none of their business. Then the First Minister phoned everyone, which was too late.

“Now the Government is involved, it needs to stop Thursday's strike.”