There is a workaround but it has 17 steps which must be followed exactly. Apple iOS 9.3 Update: New Fix For Serious ProblemsI have just read that bookings.com is being identified as the culprit. Something was wrong with an update that caused the problem identified by twerppoet (previous post). Bookings .com is now fixed, Apple must fix the universal link protocol.
To get the problem you had to have used bookings.com after the offending update, thus the reason why some are impacted, others not.
Those with the link problems might give clearing history and data in Safari's settings and see if that helps. Especially if the problem is site specific (here).
Edit: Never mind. I'm seeing news stories saying this is a widely known problem with the iOS 9.3 update (for some peope). The abover suggestion probably won't help, though it might still be worth a try.
I'm a bit behind in my news reading to day, mostly because I was burried in a good book
That's great! Thanks for letting us know.Fixed!