More than a quarter of Bulgarians questioned in a BBC survey said they intend to come to the UK to work.
An initial poll carried out for BBC Newsnight by Vitosha found that one in four people in the country wanted to take advantage of a relaxation in restrictions which come into effect next January.
A second survey carried out a month later, in March, to delve into what concrete plans people were actually making found that 4.7% were in contact with people in the UK about moving over while 2.8% were in contact with recruitment agencies. The UK was the first-choice country to move to for 9.3% of Bulgarians and 4.6% of Romanians.
A survey in Romania for the programme, carried out by Gallup, found that 1.5% were in contact with people in the UK about moving over and 0.3% were in touch with recruitment agencies while 0.7% were looking for work independently.
Work restrictions were placed on Romania and Bulgaria when they joined the European Union in 2007 but they end this year.
The surveys of more than 1,000 people in each country must be treated with caution, according to analysts.
Peter Flade, director of Gallup UK, told BBC Newsnight: "I think if you're looking at who's making concrete plans, say who's spoken for instance to a recruitment consultancy or who has a firm job offer, I think yes the sample sizes there are a bit small to say specifically who are the numbers who are coming."
It comes as MPs prepare to debate the possible impact of immigration from Bulgaria and Romania.
Conservative MP Mark Pritchard said: "EU migration has had a real impact on many communities throughout Britain. There are genuine concerns about the number of new Romanian and Bulgarian migrants likely to enter Britain when the transitional border controls are lifted later this year. EU migration has brought many benefits to Britain - but there are also dis-benefits.
"This is a debate that needs to be had - and meaningful policies put in place to protect social cohesion, public services, and to restore public trust in a workable, credible, and well-managed migration and immigration system. The coalition Government has made good progress - but there is still more to do".