So do all legal gun owners need regular psychiatric testing
as a condition of ownership
An application for a shotgun certificate needs to be countersigned by someone who has known you for at least two years and is a person 'of some standing', by which they mean a doctor, lawyer, minister of religion or other professional. You also have to state if you have suffered from any illness (including mental) and give the details of your doctor, which the police may choose to follow up. There is no testing per se.
For a firearms certificate (for rifles) you need to supply two character witnesses and to show that you have 'good reason' to own the weapon and somewhere where you may legally use it. But, again, there is no testing.
it is a also a legal requirement for any gun owner to keep the weapons safe. This has been interpreted by the police and Home office as meaning in a steel safe securely fixed to the fabric of the house with at least two five-lever deadlocks.
Effectively you won;t get a licence until the police have been to our house, approved all the locks and security arrangements and seen that you have an approved gun-safe fitted and working.
Thus it's actually rather rare these days for legitimately owned guns to be stolen. It's a lot easer for a criminal to pay £60 on the black market for a reactivated Russian or Chinese pistol (shipped in by the container-load) than it is to break open a gunsafe and then saw up a double-barrelled shotgun.