St Mary's Hospital was not government controlled or funded when Fleming was working there. It was one of the 'voluntary hospitals' supported by philanthropy and private donors. Furthermore, if you read the history of penicillin [1] you can see a long history of tinkering (meaning the discovery was somewhat inevitable) and that Pfizer, Inc. worked out how to mass produce it.

But you know, whatever...

[1] http://en.wikipedia.org/wiki/History_of_penicillin