I would not go as far as to say there are any large “no go” areas in London, but there are certainly small pockets where the minority of people would certainly feel extremely intimidated. Areas that immediately spring to mind are some parts of Stockwell, Brixton, Kennington and Camberwell as well as some in Tottenham, Edmonton and Wood Green. There are a number of London Boroughs where “white British” people are considerably in the minority. There are more where the breakdown of ethnicity in schools shows a significantly larger proportion of minority ethnic pupils than white British (indicating that the minority ethnic proportion of the population is on the increase).
Whilst em has rightly said that there are not large parts of the capital where one “will not see a white face” there are certainly areas of significant size where almost all traces of white British inhabitants have disappeared. If the London Borough of Newham is examined you will find that only 29% of the population is white and only 16% white British. 43% are Asian and 20% Black. However, Newham is a large borough and certain areas of it tend to contain people predominantly of just one ethnicity. If you travel from East Ham, along the Barking Road towards Upton Park and Plaistow it is very likely that virtually everybody you encounter will be Asian. It is perfectly understandable for white people, in particular white British people (who remember only make up one in six of the entire Newham population) to feel alienated by this. Not everybody has the attitude that the UK belongs to all comers and many feel that “their” area is being (or already has been) overrun.
All this reinforces the suspicion of "white flight”. The plain fact is that large numbers of people are not fond of living among people that are unlike them. This is not restricted to white people. You find Africans who hate Caribbeans, Caribbean’s who hate Asians, Pakistanis who hate Indians, Protestants who hate Catholics, Muslims who hate Westerners, arabs who hate Jews. The list is endless. Governments cannot legislate against these dislikes. The end result is that groups who are alike tend to congregate together. All groups are guilty (if that is the right word) of this and no government is going to prevent it (short of introducing compulsory relocations for millions). It’s what happens when large numbers of people from different nations come together over a relatively short period, especially when integration has not been facilitated or even encouraged by successive governments.