This is interesting, my parents lived on the boundary of Nelson and Burnley until 1957 a few years before I was due to take the 11+. I actually attended a CoE primary school although my parents were advised to move me to a larger primary in North Burnley well before the age of 11 as their pass rate was much better!
Few ideas for research:-
Have a good search through the National Archives - they have a lot of material http://www.nationalarchives.gov.uk
Try the archives of few local newspapers (Burnley Express etc)
Probably your best bet is too try looking at the local Grammar School web sites (Burnley Grammar, Colne Grammar etc). They probably have records of the number of pupils and you should be able to calculate the pass ration from the census figures for that period.
You comment about the Mills got me thinking; my aged Auntie (now 95) recalls the fact that she was one of the few to pass the exam for the Burnley Grammar School but wasn't able to take up her place as my Grandparents couldn't afford it. She went to work in for a seamstress instead.
Best of luck