At March 2017, the total fleet size for all TOCs was 13377 vehicles. Obviously not all of them will be in service on any given day.
I obviously did not myself clear. Is it possible to study all the timetables to work out how many different trains are running at a particular time? Has anybody tried?
Perhaps you need to define what you mean by 'trainset'. Do you mean units? A train? Your most recent post would suggest you want to know how many trains are in public service at one particular moment?
Train set is correct terminology:
train set
noun
1.
a set of railway wagons or carriages, often with a locomotive, coupled together for a particular service.
2.
BRITISH
a set of trains, tracks, and other items making up a child's model railway.
When somebody says "We are running more services than ever before" or some such, where are the statistics to prove it?