This one was frustrating, but I blundered into a solution after a minute or two. I imagine it’s a problem with iOS7 rather the phone. First of all I checked all the settings and everything was ok – but STILL the phone wasn’t ringing.
If you’ve checked that a valid ringtone has been selected – super. Next try this, call your phone, wait for it to vibrate. Whilst it’s vibrating switch the ringer (that’s the button on the left hand side at the top) to off, then switch it back to on again.