Up to 200,000 civil servants were taking part in a one-day walkout in a bitter row over pay, jobs and privatisation of public services.
The Public and Commercial Services Union said it expected up to half a million tax returns could be delayed or disrupted because the action was being held on the self-assessment tax deadline day.
Museums and galleries were also expected to close today because of the walkout, which will be followed by a two-week overtime ban and further industrial action.
Driving tests were expected to be cancelled and the union said it expected benefit offices and job centres to close for the day.
Picket lines were mounted outside Government offices and at ports, courts and museums, and a series of demonstrations and rallies were planned across the country throughout the day.
Union officials mounted early morning picket lines outside the headquarters of Government departments in Whitehall, including the Treasury and Education Department, as well as outside the British Library and National Gallery.
The union's general secretary, Mark Serwotka, was leading a protest march from the Treasury in Whitehall to a nearby rally later today where some of the country's most senior union leaders were due to address strikers.
A number of Labour MPs pledged to join pickets to show their support for the dispute.
Mr Serwotka said: "The strike shows the depth of anger over the damage that crude job cuts are having and the growing frustration over below-inflation pay offers."
The Government said there was no need for the strike and told the union the Civil Service could not be immune from the need for change.