I think the current restrictions on firearms are just about right in the UK. I don't think making them stricter would reduce gun crime (as relatively low, and most firearms used in crimes are likely not legally kept anyway), but they definitely don't need to be less restrictive.
Only thing I'd say is it would be better if there was actual proper follow through on processes by local firearms officers. Dh has guns. We've lived in 2 houses since we last had anyone turn up to inspect them or meet with us. The last house (6 years ago), it took nearly a year to even get a response to the notification that the guns had been moved and no one came out to inspect them in the 4 years we lived there. And we moved over a year ago to our new house (different county) and still no response by the local firearms officer and probably won't come out to inspect here either. My assumption was they needed to come view the set up and check all was okay (as always what they've done in the past). I don't know if this has been scrapped by COVID? Dh is absolutely fastidious about how his guns are kept and very careful, does everything by the books. But I can see that without following through on inspections and license renewals, etc. there are potentially people who could fall through the cracks, and I think this is probably especially the case post-COVID, when we've seen increases in substance misuse and poor mental health. I suspect there needs to be resources put into making sure everything is up to date and everyone who needs a check in by the firearms officer has had one.