They also without exception DO NOT care what subject you read at university, they are not hiring you for your knowledge of a particular subject! That is what the professional training is for i.e. Chartered Accountant, chartered manager, CIPD, DipLaw, etc
I have to take issue with this - many graduate programmes do indeed care where you studied, what you studied, and what your knowledge is. For example, you cannot become a chartered engineer without having read engineering; law firms typically prefer law and similar social science degrees, and investment banks take a large number of economics and finance graduates.
While there are of course the linguists that practive international banking, artists in accountancy, or mathematicians in law, the avst majority of those taken on grad schemes for professional qualifications tend to have a background in similar degrees.