Ministers are attempting to split off striking teachers from other public-sector workers as part of a strategy to divide the union movement and prevent further mass walk-outs.
Teachers' leaders are due to sit down with government negotiators today for further talks on the details of a new pension scheme. Sources on both sides said the talks were at an advanced stage and "progressing well".
Ministers are keen to do a deal with at least one set of public-sector workers in an attempt to split the union movement and put pressure on others to accept a deal. That eagerness will only have increased last night as it was reported that police officers in London had been drafted in to ferry people to hospitals in the absence of striking ambulance workers, suggesting the strength and effectiveness of yesterday's strike action was greater than first thought.
The teachers' pension scheme has been identified as one of those where it is easiest to reach agreement and the Treasury may be prepared to make further concessions. Asked if the Government might do a deal with one section of public-sector workers and not others, the Prime Minister's official spokesman said: "It is possible."
Yesterday's strike closed 62 per cent of schools in England and Wales entirely with only 16 per cent operating normally. Ministers accept that the closures had a significant economic impact as parents had to take time off work to look after children. They believe the impact of other striking workers was less.
The Government claimed only a quarter of civil servants had not turned up for work and just 19 out of 900 Jobcentres had closed. It added that there had been no serious disruption at airports and contingency arrangements appeared to have "worked well".
David Cameron claimed that industrial action was "looking like something of a damp squib". However, the unions said reports from picket lines showed a "huge" turnout, with up to 90 per cent of staff in some departments, including Revenue and Customs, striking. More than 1,000 rallies were held across the UK, including one in central London attended by tens of thousands.
"I have been to pickets around central London and spirits are sky-high," said Mark Serwotka, general secretary of the PCS union.
In a statement to the Commons, the Cabinet Office Minister Francis Maude condemned strikes as "irresponsible, inappropriate and untimely" and said there had been "a low response" from public servants.
But the teachers' strike was well-supported and the Government believes if a deal could be done with them, other workers would find it more difficult to continue with industrial action.
Unison officials – who represent many of the most poorly-paid public-sector workers – admit it will be difficult to call their members out on more strikes due to the financial strain it imposes.
Education union leaders are due to meet civil servants this morning, before going on to have their own summit on how to follow up on yesterday's action. The Schools Minister, Nick Gibb, said he felt progress was being made.
Some union leaders believe it would be possible to agree options in the separate talks over teachers' pensions.
"I think that's what's likely to happen," said Russell Hobby, general secretary of the National Association of Head Teachers. However, they believe Chancellor George Osborne's Autumn Statement has made that harder with his announcement of a further two years of caps on public-sector pay.