The Office for National Statistics said 141,000 were employed during the period from April to June, an increase of almost 26 per cent on the 112,000 in the previous three months.
This represents a rise of 35 per cent from the same period last year.
Laws restricting the types of jobs migrants from the two countries can do will be relaxed from the start of next year in light of EU rules, prompting fears of a sharp increase in numbers coming to Britain.
Sir Andrew Green, chairman of Migration Watch UK, said: “This increase of just over a third in Romanian and Bulgarian workers in the UK over the past year is a sharp increase on the previous trend.
“It suggests that still larger numbers will arrive next year when our labour market is fully open to them.
“This is consistent with our central estimate that net migration from Romania and Bulgaria will run at about 50,000 a year for the next five years.”
The government has so far refused to put a figure on the number of people it expects to come to the UK when the labour market becomes fully open to the two countries.
Officials from Romania and Bulgaria have repeatedly attempted to allay fears over a wave of immigration from their countries.
Earlier this year Bulgarian ambassador Konstantin Dimitrov estimated between 8,000 and 10,000 would enter Britain during 2014, while ambassador Ion Jinga predicted 20,000 might arrive from Romania.
A new Immigration Bill announced in the Queen’s Speech will make it easier to remove people from the UK by limiting rights to appeal and tightening the use of human rights law, as well as access to healthcare, prompting fears sick people may not seek treatment.
Shadow immigration minister Chris Bryant MP said: “How can local areas make proper plans to avoid pressures on infrastructure or public services if the Government refuse to publish their own estimates of the numbers they expect to arrive?
He added: “The Government need to address these issues and it’s clear from the figures released today that they need to do this now and not wait for January 2014.
“They should be taking action now to prevent any increase in exploitation of migrant workers distorting the labour market yet further next year.
“And they are still doing nothing to address enforcement of the minimum wage, use of agencies targeting only foreign workers, or training and skills shortages in key sectors like hospitality.”