It's an old bug from an earlier IOS version that seems to have returned.
Basically links in emails no longer work. So URLs won't activate safari. Have tried many different emails, have shutdown and restarted the phone. Have of course closed down the mail app. Nothing gives. Yet everything works fine on my iPad pro which is also running 9.3.
Full version is 9.3(13E233) on the iPhone.
Full version on the iPad pro is the same.