There is no guarantee that it will be reported if someone recovers because people do have a right to keep their health private in this country.
It's worth remembering that since there are so few cases out there, information can easily be personally identifying. The stigma from having the virus could have a detrimental effect on you in the long run. Imagine being the person labelled as the one who 'brought the plague to the uk' in the press.
Certainly the press can not legally give updates at this stage without the explicit consent of those affected.
Those in York affected have some additional factors to consider.
The press won't be able to approach them in quarantine and they are less likely to have British friends and family to pass on information. There may be something of a language barrier. And there maybe some concerns about what happens to them when they return to China because they have had coronavirus. Their privacy over their health might also be a matter of personal safety.
Whilst it might not be reassuring that you've not heard anything, you also need to consider that a 'media blackout' is part of our right to privacy of health which protects us all from discrimination and any exceptions to this rule have to be carefully considered. If someone does become seriously ill, the risk of long term complications arises so there is reason to avoid stating this publicly. Being vague and releasing only the bare minimum of information is consistent with this concern.
Equally, the way I view it, no news is good news. It would be reported if someone had died. They haven't.
I therefore don't put the lack of update down to a 'media silence' but down to the UK government and the law protecting people at a point of vulnerability in their lives and protecting their long term interests. Which I'm glad of.
If the situation changes and its felt to be essential for us to know what's going on, then this might change. But as it stands what 'need' is there for us to know more? Trying to satisfy general anxiety of the public could have exactly the opposite effect.