The government has failed to introduce measures to protect the rights of low-skilled British workers whose jobs may be threatened by new migrants from eastern Europe, a Labour shadow minister has claimed.

As Britain opened its borders to Bulgarian and Romanian workers on New Year's Day, David Hanson, the shadow immigration minister, said the government has ignored calls to strengthen existing legislation that could stop employers from undercutting British employees' wages by recruiting from overseas.

His comments came as the first Romanians and Bulgarians with unrestricted access to the UK labour market began to arrive amid a deepening political row.

All political parties are aware that the possibility of high numbers of new migrants has become an issue, fuelled by unproven claims that the new arrivals could lead to a rise in crime and social problems.

Romanians landing at Luton airport on Wednesday were greeted by the home affairs select committee chairman, Keith Vaz, who said they provided just a "snapshot" of those expected to come to the country over the coming months.

The 180-seat aircraft from Târgu Mureș, Romania, had only 140 passengers on board, he said, most of whom already live and work in the UK.

"Just on the conversations we've had with people who have come here, a lot of them are returning people, they already work in Britain and they're coming back after a holiday so they're not people coming here for the first time," Vaz said.

"We've seen no evidence of people who have rushed out and bought tickets in order to arrive because it's 1 January.

"We'd be surprised if they did so, this is after all only a snapshot. But we do need to resolve this issue in the future, and it's an issue for the whole of the EU to resolve so we don't get these kinds of dramas at the end."

Hanson, interviewed on BBC Radio 5 Live on Wednesday, said the government had failed to introduce a series of measures to slow the recruitment of low-skilled workers from eastern Europe.

"We have been arguing for the past year that [the government] should be looking at other measures such as enforcement of the minimum wage, such as extending gangmaster legislation to areas such as catering and tourism, and particularly focusing on recruitment agencies which are recruiting solely from eastern Europe. Those are other measures we could be doing to focus on low-skilled immigration," he said.

Hanson also claimed that some of the rhetoric employed by Tory politicians had turned the issue of migration controls into a frenzy: "These controls have been lifted across the whole of Europe. We should not have a frenzy, we should have a calm, measured approach," he said.

Romanian representative Roxana Carare, an honorary consul in Britain, said the number of people travelling to the UK would not change, but added that there was demand for Romanian and Bulgarian labour.

"The numbers haven't changed because people have been able to travel since 2007," she said. "But I hear that people are being recruited, so they are coming in response to the demand for work. Romanians are being recruited by work agencies from everywhere in Europe, not just UK agencies.

"It's down to the employer to decide who they are going to offer a job to, but if agencies are going to recruit workers from Romania then there is a reason for that."

Speaking to the BBC, Carare added that countries that offer employment training would prove the most attractive to Romanian migrants.

"For labourers, and other skilled workers, countries that they can relate to, from a cultural and linguistic point of view, [will be the most attractive]. Britain is not top of the list because this is Anglo-Saxon country and Romania is a Latin country. People are more likely to go to Italy, Spain and other Latin countries."

The Guardian disclosed on Tuesday that MPs on the all-parliamentary party group on Gypsies, Travellers and Roma have expressed alarm about provocative language, as a prominent Tory council leader in suggested some Roma were planning to come to the UK to "pickpocket and aggressively beg" following the end of labour market controls on the two countries.

Ahead of the lifting of the restrictions, Philippa Roe of Westminster city council blamed Roma in central London for already causing "a massive amount of disruption and low-level crime", including defecating on doorsteps. Speaking to the BBC, she called for more limits on benefits for new arrivals from EU countries and claimed there would be rising costs in council tax unless the government offers financial help.

"I know the vast majority of Romanians and Bulgarians planning to come to the UK are planning to work and contribute to society here," she said. "But I think the fear that everybody faces is those that come to Britain and either fail to find jobs and therefore fall back on our welfare system, or those who deliberately come here to pickpocket and aggressively beg.

"We have seen in the past 18 months particularly the Roma in central London causing a massive amount of disruption and low-level crime which has made a very negative impact on our communities. It's this minority one is really concerned about but it is this minority that has this really big impact."

Ninety senior Conservatives attempted to block the lifting of the restrictions in a letter to David Cameron, arguing he could invoke a clause in EU law to keep the borders shut.

But ministers denied such a move would be feasible.

Vaz spoke out against the government's refusal to bow to repeated demands to publish or commission estimates of the numbers expected to enter Britain after unofficial research predicted as many as 50,000 people would arrive from Romania and Bulgaria each year.

"The concern of the committee has always been the lack of robust estimates of people coming here and we still feel very strongly the government ought to have asked the migration advisory committee to have conducted a piece of research which would have told us the number of people who were came into this country or were coming into this country.

"We think that would have been extremely helpful. The fact that we don't have those estimates means that we have this kind of drama at the end, which is not helpful to anybody," he said.