Firstly, I don't buy the argument that new Acts of Parliament are needed for this. The mess that firearms licensing is in is not a result of the primary legislation, it is a consequence of poor administration (surprise surprise). All of the dysfunctional elements have been devised and implemented by either police forces or the Home Office. I don't think there's anything that couldn't be sorted out by Statutory Instruments or revoking existing ones.
Public safety isn't first, the law is. Second is making sure it is effectively implemented. Public safety is important, but it's just one factor. The most important thing is that you have a functional system which adheres to the law, doesn't create arbitrary nonsense and that this is done by dealing with the problems with the current system:
1. Inaccurate record keeping by police forces, and a possibly .
2. Arbitrary and unnecessary rules creating unnecessary work and choking up the system.
3. Pointless, slow, expensive and dysfunctional medical requirements.
4. Some forces having bizarre system of "approving" land suitable for shooting on.
5. Unnecessarily pedantic approvals for specific calibres.
6. 1 for 1 variations.
7. Moderators.
8. Ignorant pretence that X calibre is more dangerous than Y calibre.
5. Five year renewals.
and probably more.
Further problems include forgery of paper certificates, sometimes people failing to update police in time of purchases/sales, and the departments running the system being overworked, undertrained and generally low-grade.
The solution is then obvious. Take administration of the system away from the groups who caused the problems and instead give them oversight.
1. Introduce an online system, with either cards or use of an app - as per everyone's banking system which has worked pretty flawlessly for decades.
2. Get rid of paper certificates which are wildly out of date and a security risk to the holder. Replace with a card or app based system which does not display to everyone what your home address is. This solves completely the problem of forged certificates.
3. Since we have continuous monitoring of holders, there is no need for a renewal process and certificates can last until the holder is 75 at which point a renewal seems reasonable.
4. Take the administration of licensing out of police control and have a body co-operatively owned by the certificate holders own and administer it. The role of the police is then freed up for monitoring and investigating cases of concern properly, and they can enforce action against the licensing body if it doesn't do its job properly. The co-operative could also administer a comprehensive insurance scheme wrapped into the same fee so all shooters are covered.
5. Get rid of most of the work that licensing departments do, which is ludicrous, pointless and useless work - approving land as being suitable for X calibre or Y calibre. Making judgments about medical conditions which they are unqualified and incapable of doing properly, variations and approvals for specific calibres - these can be grouped into broad bands - rimfire or centrefire. Beyond that there is no major real difference in risk. All the rest is a waste of time and effort. Abolish the need for 1for1 variations to be approved beforehand.
6. Tighten up the time requirement for informing the police. Seven days was appropriate when it was done by mail. Nowadays there is no reason why it should not be done at the time of transaction in an RFD, or at the least within 24 hours. Private sales, I'd think perhaps would be better done on an RFD's premises anyway.
7. Explore whether the same or a parallel system ought to administer and vet police officers' access to and use of firearms, given the slew of recent scandals involving armed officers, and the fact that the majority of firearms discharged at people in the UK are fired by the Police. This fact is usually obscured by the Police and Home office by the sneaky practice of the word "firearm" being very differently defined for use by the police and by the public.