A quarter of a million Romanians and Bulgarians are now living and working in Britain, more than 80% of whom arrived before labour market restrictions on migrants from their countries were scrapped 12 months ago, say academics.

The Oxford University-based Migration Observatory said the growth in the Romanian and Bulgarian populations of the UK had remained at the same steady pace for the last seven years.

The lack of a surge in migrants from the two EU countries after seven years of transitional controls were lifted on 1 January 2014 confounds predictions by Ukip’s Nigel Farage and others that 5,000 Romanians and Bulgarians would arrive “each week, every week” for several years.

The migration experts said the latest labour force survey figures showed that the overall population of Romanians and Bulgarians in the UK rose from 205,000 in September 2013 to 252,000 in September 2014, an increase of 47,000. This followed a similar rise of 45,000 in the corresponding period in 2012-13.

Madeleine Sumption, the Migration Observatory director, said: “The growth in the Romanian and Bulgarian population of the UK has been steady for the last seven years, despite transitional controls that limited their access to the labour market and welfare state in the UK. The end of these controls do not seem to have had a very significant effect.”

She said immigration from the two countries had been much more gradual than flows from states that joined the EU in 2004, such as Poland.

“In 2004, the UK was one of only three EU member states that did not introduce transitional labour market controls on migrants from new accession states and saw a sharp increase in migration from these countries. It seems likely that the controls imposed in 2007, together with a weak economy at the end of the decade, may have slowed the pace of Romanian and Bulgarian migrants settling in the UK,” Sumption said.

When the transitional controls were lifted at the beginning of 2014, ministers refused to release any estimates of how many Romanians and Bulgarians might come to Britain. This triggered a lot of speculation about the likely numbers, with the highest predictions coming from Ukip candidates and rightwing Conservative MPs.