More statistics are being released recently from the 2011 Census with much more focus on ethnicity. Just as with the growth of the population in the UK, the Chinese population saw an increase from 5% (247,403) back in 2001 to 7% (393,141) according to the latest stats. That's about 58% increase in the past 10 years. However there's no further breakdown of the subgroups such as the nationality or place of birth, but I'm guessing the increase in population is largely due to the influx of immigrants particularly from mainland China. Undoubtedly the population of British born Chinese will also have increased and more or less contributed to the growth.
We often consider British Chinese to be the third largest ethnic minority group in the UK but when you start breaking down Asian and Black into other subgroups it is no longer the case. As for other East Asian groups the details are even more ambiguous. So far there aren't many other details in regards to the lifestyle and well-being of any particular groups. Again, we'll have to wait for the next batch of statistics to be released. But we can certainly say that the British Chinese community is still thriving.
Brief overview of the 2011 Census on ethnicity
More info from the BBC News site