Most of the seniors from my school went to study in America around 1980s when I was still in school, so your information about people migrating to US in 1990s is incorrect and also the influx of students to UK started around 2000 and mass exodus of Gurkhas happened recently i.e. since 2005 (before that everyone had to return to Nepal after serving for certain number of years).

As far as I can remember from 12 years back, there were around 20k Nepalese in UK and you could hardly find any nepalese here while 7 out 10 people used to go to America for studies at that time which I think holds true now as well, ignore the DV Lottery.

Your figure may be right but it surely accounts for people living there legally.