A top Tory warned that a minority of the immigrants from Romania and Bulgaria could escalate existing problems, including pickpocketing and defecating on doorsteps.
Philippa Roe, Conservative leader of Westminster City Council, told BBC Radio 4's The World At One programme: "I know the vast majority of Romanians and Bulgarians planning to come to the UK are planning to work and contribute to society here.
"I think the fear that everybody faces, which is reflected in the media, 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.
"You've only got to wander around Marble Arch at 7.30 in the morning to see the camps.
"We have people walking out of their front door to find people sleeping on their front doorsteps, people defecating on their front doorstep.
"It's extremely unpleasant and it goes with the very aggressive begging and pickpocketing and other sorts of crime in the area which affects both residents and tourists."
An easyJet spokesman has said that the airline has not seen any increase in passenger numbers from Bulgaria or Romania to the UK.
He said: "EasyJet currently only flies to two destinations in Bulgaria and Romania and other airlines provide far more frequent services.
"We haven't seen any evidence of an increase to our passenger numbers from January 2014 on these routes."
A spokeswoman for the Romanian foreign ministry has dismissed claims that the UK could see an "invasion" of migrants and said that some media reports have bordered on racism.
Brandusa Predescu told the BBC: "There isn't going to be an invasion of Romanians ... Not all Romanians, young and old, are going to get on a plane.
"The UK will [not be] and is not the preferred destination of Romanians," she added.
Romanian and Bulgarian migrants bring "knowledge and experience" London businesses "badly need" and fill a skills gap that British youngsters cannot, The London Chamber of Commerce has said.
Chief executive Colin Stanbridge said:
Political rhetoric on migrant workers has stepped up in recent days as the deadline for removal of restrictions approaches. However, the debate often fails to take into account the positive benefits that migration brings to the London economy.
Migrant workers are often highly skilled, bringing with them knowledge and experience that London businesses badly need - now - in order to continue to grow.
Of course the Government needs to equip our young people with the skills that businesses require, but that will take years.
Experts predict 250,000 Romanian and Bulgarian migrants will move the UK over the next five years when restrictions on entry to the UK are lifted on January 1.
According to a report by Migration Watch UK:
- A Romanian with two children and a spouse on the average wage in their home country will take home £4,000 after tax
- A Bulgarian in the same circumstance will take home £3,800
- Even if they were still on half the average Romanian or Bulgarian wage, that worker will be six times better off in the UK
- They are three times better off in Spain or Italy
- Germany is the "most attractive destination" as it has a low unemployment rate and large number of vacancies
Romanian and Bulgarian immigrants will still see the UK as the most attractive EU country because of "generous" in-work benefits, a study has claimed.
Migration Watch UK has warned that new curbs to tackle benefit tourism will not deter Balkan migrants because reforms only prevent migrants from collecting out-of-work benefits.
Romanian and Bulgarian migrants already living in Spain and Italy may come to the UK when restrictions are lifted on January 1 because there are "considerably greater" financial rewards.
Migration Watch UK chairman Sir Andrew Green said: "This study shows how Britain's generous benefits system acts as a pull factor for migrants from across Europe.
"There must now be a renegotiation of the benefit system in the EU which was designed before 100 million people in much poorer countries joined the EU. British taxpayers must no longer subsidise immigration from poorer parts of the EU."
The British public should worry more about bankers who make off with taxpayer millions and less about Roma who beg on the streets, an aide close to the Romanian prime minister has said.
Damian Draghici, who is an adviser on Roma affairs, predicted that only around 2,000 to 3,000 would travel to the UK after restrictions are lifted on January 1 as Britain was too cold.
He told The Times (£): "The Roma begging in the streets are obvious because we see them, they ask for one pound or one euro and they bother us.
"Yet some of the people in the banks are stealing billions of euros but nobody sees them because they are on the 60th floor".