Yep - the News Corp / News International / BSkyB fork means that it's going to be tricky to implement "Fit and proper" - unless it can be proved that News Corp management were aware of the News International illegalities I guess.
As News International is essentially a fully owned subsidiary of News Corporation, it could just be a case of follow the ownership and the personnel. James Murdoch is the Chairman of British Sky Broadcasting, Chairman of News International, Chairman and CEO of News Corporation International, and Deputy Chief Operating Officer of the main News Corporation. as well as a member of the main News Corporation Board. He is tied into all three parts of the Murdoch empire under controversy at the moment. There is a section of the UK Regulation of Investigatory Powers Act that would allow board members to be charged if they neglected their duties allowing illegal activity covered by that Act to take place, which would apply to James Murdoch as a board member and Chairman of News International, and as already noted there is the possibility of an American investigation into corruption.
The trouble is though with the monopoly Sky has if it did go out of business it wouldn't be good news at all for British television in the short term at least with consequences for millions of Sky subscribers and multiple satellite channels. And whenever anything did rise from the ashes to fill the void left by BSkyB, it would almost certainly be of a similar model anyway.
BSkyB as an entity separate from News Corp. is very profitable. In the short-term, if News Corp. were forced by being found not to be fit and proper to control UK broadcast licenses to give up either enough shares so that it no longer had effective control, or divest of all its shareholding entirely, it would have no effect on BSkyB as it is capable of standing on its own two feet.
In the medium to long term, it would start to have consequences in terms of the relationships with other News Corp. properties, meaning they wouldn't enjoy privileged relationships with the likes of 20th Century Fox when importing U.S. TV programmes and movies.