Fox currently has a 39% stake in Sky, and has been trying to buy the remaining 61%. However, the Competition and Markets Authority in the UK (the CMA) has said such a deal would not be in the public interest thanks to media plurality.
The Murdoch Family Trust which currently controls Fox, also has control of several other major news outlets in the UK — The Sun, The Times and Fox News to name but a few — and should it come to own the entirety of Sky, it would have too much control over news broadcasting (and therefore too much control over political agenda and public opinion).
Other than the issue of media plurality, however, the investigation carried out by the CMA found that Fox's commitment to broadcasting standards in the UK are more than adequate and in that regard, its control of Sky wouldn't be against the public interest.
Of course, Fox recently agreed to a deal with Disney, in which Disney is to buy most of Fox's business — so if the Sky/Fox deal was to go through, it's likely that Sky would become a property of Disney.
In light of that, the CMA will continue to investigate and will set out its final report on 1st May. It has set out potential remedies for addressing the issue of media plurality, and both Sky and Fox will engage with the CMA during this time until a final decision is made. [BBC via Gov.uk]