With less than two months to go until Romanians and Bulgarians gain free access to the UK employment market, the media campaign against them is well under way. "Allowing this new flood of migrants is economic lunacy," wrote Ukip's Nigel Farage this week. The day before, the Daily Mail had reported: "Recruitment firms are being inundated with requests from Romanians about how they can claim benefits in Britain."

As a Romanian living in Sheffield, I know people are already worrying whether my compatriots are going to swamp this island on New Year's Day. Not long ago my neighbour called over the fence to ask: "How many more of you lot are heading this way, then?"

She was surprised when I said I didn't know. The truth is that no one knows. As a spokesman for the Foreign Office told me this week: "There are no reliable statistics about the number of expected Romanians in the UK. It is a complicated issue involving a number of factors, and any figures would only be a guess."

I decided to take a trip home recently to try to answer my neighbour's question with a more educated guess.

First I met Ion Cristoiu, one of the best-known journalists in Romania, the founder of several newspapers and a producer of TV political broadcasts. He was clear that the shrill headlines in the UK media do not match the reality. "The immigration phenomenon is a complex one but the implications have already played out. Lifting the restrictions is not something of interest for Romanians any more," he said.

Most employment agencies in Bucharest that I contacted – which specialise in placing jobseekers overseas – report no particular spike in applications from jobseekers hunting for jobs in Britain after 1 January.

Camelia Mihalcea, manager of Eures Romania, a public recruitment network in Romania co-ordinated by the European commission, said she had received only a few emails from British recruitment agencies looking for skilled workers to place in the UK. This week Eures was advertising five UK jobs in the social care sector, starting in 2014. One was based in Norwich, working for the UK recruitment agency Jark, offering £12-£24 per hour for qualified nurses.

She said she had had just 20 requests this year from British public or private companies looking to recruit from Romania.

Nicole Atomei, manager of Krevin, a private recruitment agency in Bucharest, said she had placed only 15 Romanians so far in 2013 in the UK, mostly in the hospitality, agriculture and social care sectors. She said she was expecting to send at least another 15 in the new year, to work in hospitals and telecommunications. She'd had far more requests for people to work in Belgium and France than in the UK, she added.

Nor is there evidence that many Romanians are brushing up their English to prepare for work in Britain. According to the British Council in Bucharest, there has not been a significant increase in students enrolling for the main English-language proficiency tests, the International English Language Testing System (IELTS). An IELTS certificate is often required by UK institutions, employers, professional registration bodies and government immigration agencies as part of their recruitment or admission procedures.

There is no doubt that wages are much better in the UK than in Romania. "The farming sector offers jobs in the UK with wages of £900 a month, which is equivalent to 4,500 RON [lei]. An agricultural worker in Romania would get a salary of 2,000 RON," said Atomei. A social worker in the UK gets a minimum of £12 an hour or more, while in Romania they receive no more than £2 an hour.

But the economic situation in Romania is slowly improving. According to the National Institute for Statistics in Romania, in the first quarter of this year the GDP rose by 0.5% compared with the fourth quarter of 2012 – when there had been growth of 1.1% on the third quarter of the same year. The unemployment rate fell by 4.73%, according to statistics published on 30 September 2013, with urban areas doing much better than rural ones. About 5% of the economically active population in Romania are unemployed, compared with 7.7% in the UK.

Mariana Câmpeanu, the Romanian minister of labour, accused UK media of exaggerating: "I would like to say that it is an overreaction, and totally unjustified. Nothing shows that Romanians express a huge interest to work in the UK. It is obvious that those who wanted to leave Romania for the UK have already done it. This hysteria is completely wrong".

The stereotype of Romanians in the UK is of low-skilled workers, perhaps fruit-pickers or other seasonal workers. But some of the brightest Romanians see Britain as a place to do business. Take Nicolae Olariu, 48, from southern Romania, who says that he wants to export timber from Romania to the UK.

He's not the only one. But headlines such as "Romanian entrepreneurs flood Britain to start businesses" are unlikely to be splashed over British tabloids any time soon.