Although I've found that "Profumo's responsibility was the Army, and his principal preoccupation was helping to recruit and establish a regular volunteer Army after the abolition of conscription" (The telegraph http://www.telegraph.co.uk/news/obituaries/1512656/John-Profumo.html), it seems to me that his duties included more than this.
He was in charge of the War Office, so ultimately was responsible on the civilian side for the Army in the same way as the current Minister of Defence is ultimately responsible for the Army, RN and RAF. So things that he would have had to answer for in Parliament would include:
- Development and implementation of defence policy.
- Annual budget, including new equipment purchases.
- Senior promotions/appointments (e.g. appointing the CIGS).
- All the other bells & whistles that any CEO has to deal with.