Net immigration to Britain has surged by 78,000 in the past year to 260,000 – a level substantially above the 244,000 in 2010 when David Cameron and Theresa May took office, according to the Office for National Statistics.

The figures for the 12 months to June 2014 extinguish any remaining hopes that the prime minister and home secretary could meet their target of reducing net immigration to below 100,000 by next year’s general election.

The data also shows that immigration from outside Europe has once again started to increase, alongside a rise in the number of European migrants working in Britain.

Included in the 78,000 increase is a rise of 45,000 in EU migrants and an increase of 30,000 in those from outside the EU. This undermines May’s claim to have reduced immigration from outside Europe while being prevented from curbing European immigration by the EU’s free movement rules.

The detailed figures show that an estimated 323,000 people left Britain to live and work abroad in the 12 months to June 2014. This rate of emigration has been relatively stable since 2010.

The ONS said the increase in the numbers coming to Britain to work was driven by a 14,000 rise in non-EU migrants, an 11,000 increase in Romanians and Bulgarians and a 10,000 rise in western European migrants.

However, the latest Labour Force Survey figures show that two-thirds of the extra 692,000 people in employment in Britain in the past year are British nationals. The number of foreign nationals working in Britain rose by 230,000 to 2.9 million in the 12 months to September.

The immigration minister, James Brokenshire, insisted that the government had cut immigration from outside the EU by nearly a quarter since 2010.

“Uncontrolled, mass immigration makes it difficult to maintain social cohesion, puts pressure on public services and forces down wages. This government has shut nearly 800 bogus colleges, slashed 45,000 visas from the further education route and cut family visas by nearly a third since it came to power – meaning there are 50,000 fewer migrants coming to the country from outside the EU than there were in 2010,” he said.

Brokenshire said government reforms had restricted access for illegal migrants to work, housing, benefits, and healthcare. The prime minister would shortly set out “how we intend to reform the freedom of movement in the EU that is driving the rise in immigration to the UK”, he said.

But the deputy prime minister, Nick Clegg, said the Conservatives’ failure to meet their target for reducing net immigration – which the Liberal Democrats had always opposed in government – would undermine public confidence in the immigration system.

“This was a Conservative preoccupation. They made that promise. They have now broken that promise and they will have to suffer the embarrassment of having done so,” he said on his weekly LBC radio phone-in.

“I think that it does damage public confidence in the immigration system by over-promising and under-delivering in this way.”

ONS statisticians said the 43% increase in net immigration was the second-highest annual rise on record.

The rise comes before a long-awaited speech from Cameron on immigration. At the weekend, the home secretary tried to defuse the impact of the latest figures by finally publicly conceding that it was “highly unlikely” that the government would deliver the prime minister’s “no ifs, no buts” pledge to reduce net immigration to the tens of thousands by May.

She made much of her success in reducing immigration from outside Europe and said the increase in net immigration from within Europe was due to the British economy doing much better than the eurozone.

But the latest figures show that while the number of overseas students has stabilised at 172,000, more migrants from outside Europe are coming to work in Britain once again.

The detailed figures also confirm that Ukip predictions of a flood of new migrants from Romanian and Bulgaria since the start of the year, when labour restrictions on them were lifted, were unfounded.

The latest national insurance figures do show that Romanians had the highest number of new registrations, at 104,000. But the ONS figures also show that more than 50% of these involved Romanians already living in Britain, suggesting that they were regularising their position in the hidden economy.

The quarterly migration figures also show that asylum applications remain at 24,300 in the 12 months to September 2014 – only a quarter of the level they were running at a decade ago.

Carlos Vargas-Silva, of Oxford University’s Migration Observatory, said: “The government’s own data showed in 2011 that their policies were not expected to reduce immigration by enough to hit the target. So, we have been watching a result that we have expected for three years unfold in slow motion.

“Increased EU net migration has certainly meant that the degree by which the target is missed will be much higher, but it is clear that the target would have been missed with or without this increase, as non-EU net migration alone is way over 100,000.”

Mark Hilton, of the London First business group, said the latest jump in immigration showed ministers had done the right thing by laying the coalition’s immigration target to rest. “Theresa May effectively killed the migration target off when she admitted what we’ve known for a long time – that the government was not going meet its pledge,” he said.

“Those who work to get the right people with the right skills into the UK won’t mourn its passing. Now we need to dust off the welcome mat and carry on attracting the engineers, tech experts and other workers with the skills we sorely need.”

Ukip’s immigration spokesman, Steven Woolfe, said: “This is either a total scandal or a longstanding con trick by a party who were elected on the promise of reducing immigration to the tens of thousands.

“Today’s astronomical migration figures show an abject failure by this government to control immigration, despite countless promises to the public. The eye-watering increase places immense strain on employment prospects, schools, hospitals and housing. There is nothing Cameron can say or do now that can right this massive wrong.”​