I suggest you write letters to the personnel departments at both Airports. Give a brief description of your background and aviation interests, and include the dates when you would like the work experience, but try to be flexible. I can't advise specifically about B'ham or Coventry, but periods of one or two weeks are about the norm. Spending a few days with each Airport department, not exclusively with ATC, may be offered, and can give a useful insight into civil aviation. Can you enlist the help of a teacher/careers advisor, or similar, from School ? If so, they might also write a letter supporting your application. Good Luck.