Dr Tamara Voronina's large, angular glasses cover a substantial part of her smiling face. They have large handlebars across the top in fluorescent pink plastic. Just the kind of thing Elton John might wear; and, in my stereotype at any rate, a certain kind of Russian might wear, like ironed jeans or spangly shirts.

Dr Voronina is a Russian entrepreneur who has come to work in London. She does not peddle arms, or launder drugs money. She sells diets: a new answer to obesity that she developed while working as a research scientist in Russia.

Her treatment, a mixture of acupuncture and diet based on hormone control, is becoming fashionable. She was the subject of a health feature in Elle not long ago. And she has been able to set up shop in Harley Street. Her English is still uncertain, but she is a quick learner. Dr Voronina is one of the new arrivals, one of those who went into private business after perestroika in the late Eighties and looked for opportunities abroad.

We have been told that Russians are invading Britain and bringing with them some of the criminal anarchy that is overtaking their own country organised crime, prostitution. But is this true? The English seem to think that many Russians are criminals; they do not understand how Russians can be good at she says. She is clearly doing well, and proud of it. We have to curtail our meeting because she has just had a call from a television producer, asking for an urgent appointment.

Since 1988, when Mikhail Gorbachev made it legal for Russians to go into private business, entrepreneurs have been busy. Some had an early advantage: they had been running the black market under Communism and had the ready cash and influence to grow rich quickly. They are the backbone of the new mafia that has been able to exploit the power vacuum which followed the collapse of Communism.

There is no doubting their influence. A recent report by the London-based security consultancy Control Risks Group estimated that by the beginning of 1994 there were 5,800 organised criminal gangs in Russia with more than 20 members. Two hundred of these were large syndicates with international operations.

British business people dealing with Russia are concerned. One man, who asked not to be identified, says: 'Eighty per cent of all businesses there have some mafia connection. They are there in all sorts of guises. It is the Chicago of the Twenties. I know of one businessman who was very badly beaten up in a dispute which involved less than pounds 50,000.'

There are widespread rumours of murder and extortion. Control Risks identified 7,000 extortion demands made of foreign business in Russia in the first six months of 1993.

There is kidnapping, too. The Russian managing director of a Russian-American joint venture was kidnapped near Moscow's main airport in January last year. A ransom of dollars 1m was demanded. It is not known if it was paid. But he was chained up, tortured and injected with drugs before being freed.

The gangs have taken their violence abroad, mainly into Eastern Europe and Germany, where there is a substantial Russian business community. There are concerns in Britain that the violence may seep in on the back of Russian businesses. There have been frequent media reports of extortion. Last year, two officials from the tiny Chechen republic were killed in London; then two months ago an English geophysicist, Karen Reed, the sister-in-law of one of two Armenians held responsible for the killings, was assassinated at her home in Woking. The bullets used to kill her had been drilled, filled with mercury and stopped with wax, to increase the injury they would inflict.

But were these killings really the work of organised criminal gangs operating in the UK? Paddy Rawlinson, a researcher in Russian affairs at the London School of Economics, believes not. She believes they were political, and that Britain is far less threatened than people may think.

'There are some problems in money-laundering,' she says, 'but the reason the Russians are able to get away with it is because some members of the financial community allow them to.'

The extent of laundering in the UK is disputed. Ms Rawlinson knows of phantom Russian banks being set up, and front companies opened in the UK, to wash drugs money clean. Control Risks believes that the Russians tend to launder money more often through Switzerland and Belgium, where regulations are more lax.

The National Criminal Intelligence Service, which has a unit monitoring organised crime, says the Russian gangs are not here - yet. 'What we are concerned about are threats posed in the future and that, as far as we can see, is in terms of using financial systems to launder money,' says a spokeswoman. 'Newspapers are getting very agitated about the mafia - which is not a term we would use anyway.' This week two senior officers are visiting Moscow on a fact-finding mission, she added.

There can be no doubt that the explosion of commerce in Russia has created vast new wealth for entrepreneurs, legal and illegal. But not much of this seems to be making its way to Britain. There are perhaps 20,000 Russian businesses operating in Germany but only a few dozen in Britain.

Victor Schekhochikhin is one of the new rich. He was a bookkeeper until the late Eighties. Now he is a rouble billionaire, and president of the Russian Union of Private Businessmen. He runs a co-operative agricultural business that controls around 3,000 hectares of land. He was in London last week on a visit, and he plans to open an office here. 'Britain is a nice quiet place for implementing plans, and it has a good tradition of training, like Oxford and Cambridge,' he says.

He would like his children to be educated in the UK, but like many others of the super-rich elite his wealth is not yet liquid. He still lives with his wife and four children in a two-room Moscow flat. He is building 'several mansions' in Russia, but none is finished. 'I don't know why your media says that there are so many Russians here. They are not so numerous,' he says.

They are not the new Arabs, seen as buying up large chunks of Knightsbridge and taking over British public schools. A recent survey of 374 schools showed that there were just 62 boarders from the former Soviet Union. That was a big increase on 1990, when there were just three or four, but it is hardly an invasion. Similarly, property developers report only the merest increase in house-buying by wealthy Russians.

The truth seems to be that Britain is not as attractive as the British would like to think it is. Another Russian entrepreneur says Britain is conservative, inflexible; not an attractive place to do business. 'There used to be more business between Russia and Britain, which picked up a lot of the big government contracts,' he says from his office in Moscow. 'But this is finished and Britain suffers. Everybody prefers Denmark, Holland, even Ireland.'

The prevailing view in the UK that new Russian arrivals are rich crooks is likely to turn Russian business people away. 'I have had credit refused a couple of times,' the businessman says. 'Because of these unjustified suspicions. And I do not know anyone who is rich on the scale of some British entrepreneurs.'

Perhaps it is the character of these new entrepreneurs, as much as anything they have done, that makes the British establishment nervous. They are hard, brash and ready to cut corners to get business done. 'I know one guy who comes here and buys clothes and sells them at hugely inflated prices back in Russia,' says Paddy Rawlinson. 'But is that crime? No. Maybe it's dubious. But it's just naked capitalism.'

Most entrepreneurial arrivals are, despite their enthusiasm, making only a modest living. Dr Voronina earned a decent living last year, and spent most of that on her fledgling business. She came to the UK for a holiday and stayed on.

'It is very difficult to come to England, however rich you are. I have done an impossible thing. And I am very happy. This is a beautiful country.' She has never been approached by gangsters asking for protection money; she knows nobody else who has been.

She came here precisely to avoid the instability and fear provoked by the lawlessness of Russia. And she hates the crime gangs. 'These are the people who say: Russians are good for nothing; if they are not rich they are not clever. I am not frightened. I do not have time to think about the mafia. I am getting on with my business.'

(Photograph omitted)