Basically the UK is not part of the Schengen group of countries and therefore, you cannot travel on a Schengen visa in the UK. Now you have entered in the UK with a UK visa and you further want to get a Schengen visa. If you are visting one country of the 24 states under Schengen group then you can apply in the ambessy of that country in the UK. However, if you have planned to visit many of these countries then you can apply any ambessy of the countries you want to visit, for getting a Schengen visa. In other words, yes you can apply for Schengen visa in the UK.
FAQ Schengen visa
FAQ Schengen visa