Net migration to Britain has surged by 68,000 in the past year to 243,000, leaving in tatters Theresa May's promise to reduce the figure to below 100,000 by next May's general election.

The Office of National Statistics (ONS) says two-thirds of the 68,000 increase in the 12 months to March 2014 was accounted for by a rise in European Union nationals coming to Britain, mostly for work.

Those coming from the new EU states of Romania and Bulgaria account for only 16,000 of the 68,000 rise, with the bulk of the increase from western European countries such as Italy.

The rise in the politically sensitive yardstick of net migration – which measures the number of people coming to live in Britain for more than 12 months minus the number of people going to live abroad for more than 12 months – is a major embarrassment for May, the home secretary, and David Cameron, the prime minister.

The Conservatives fought the 2010 general election on a pledge to bring net migration to "tens of thousands" by the time of the next general election.

May brought in sweeping new immigration policies to cut the flow, including a squeeze on international students and family migration, which initially cut the annual figure to 154,000 by September 2012, but since then it has risen steadily to the new high of 243,000. The Liberal Democrats have always made clear the promise was not a coalition policy.

The latest ONS quarterly estimate covers six months of the period that will be included in the final set of figures to be published before May 2015, which means not only that the Conservatives are highly unlikely to meet the target but also that the party will go into the election campaign with a net migration figure that is more than twice that level. Their only crumb of comfort remains that the figure is below the peak figure of 320,000 for the year to June 2005.

The ONS said the net migration figure was made up of 560,000 coming to live in Britain in the year to March 2014 – a statistically significant increase from 492,000 in the previous 12 months. Emigration from Britain remained stable at 316,000.

Two-thirds of the increase was accounted for by the arrival of extra EU citizens – up 44,000 to 214,000. The number of Romanians and Bulgarians coming to Britain rose by 16,000 to 28,000 over the 12 months to March, reflecting the final abolition of labour restrictions on these nationalities in January.

The number of overseas students remained stable at 177,000, with higher numbers of university students but fewer coming to study in further education and language colleges.

The number of asylum seekers in the 12 months to June remained stable at 23,479, still far below the 2002 peak of 84,132.

Mark Hilton of the business organisation London First said the net migration target should be put out of its misery. "With the general election fast approaching, the government is running out of time to hit its 'tens of thousands' target. The danger is ministers will take the only real steps open to them and clamp down on skilled non-EU migrants – who bring much-needed skills into the country – and students, who are not only an £10bn market for us, but a key plank in Britain's global influence in terms of 'soft power'," he said.

"At the very least, the government should heed the calls of a long line of politicians, committees, and experts, and drop students from the net migration target."

The Conservative immigration minister, James Brokenshire said: "Our reforms have cut net migration by a quarter since the peak under the last government - and have led to net migration from outside the EU falling to levels not seen since the 1990s.

"We are creating a system that is fair to British citizens and legitimate migrants but is tough on those who flout the rules.

"The government has reformed benefits, healthcare and housing rules to make them among the tightest in Europe and we continue to see an increase in the number of British citizens in work.

"In the past, the majority of growth in employment was taken up by foreign nationals. In the last year, three-quarters of it was accounted for by UK nationals.

"The new Immigration Act continues our reforms by limiting benefits and services for illegal immigrants and making it easier to remove those with no right to be here by reducing the number of appeals," he said.

But the Oxford University-based Migration Observatory said the rise in net migration made it "effectively impossible for the government to achieve its 'tens of thousands' target by the end of this parliament without radical measures", and was likely to be associated with the UK's strong growth in comparison to other large EU economies,