As an IT pro and graduate, I've been involved in the recruitment of programmers and the very first requirement on the job spec. is a degree or HND or equivalent level qualification in a relevant discipline. Candidates without were rejected straight away and HR would not allow them to be even considered.

When I first joined a software house in the seventies, computer science degrees were fairly scarce and they took graduates from many disciplines including music and sciences using aptitude tests and problem solving to help sift them. Computer science graduates fast tracked through though.