In a country such as the UK where police are not routinely armed I dont think relaxing restrictions on firearms is a wise idea. Culturally the UK is vastly different to the USA and with an unarmed police force the vast majority of crimes are committed without firearms and those that are happen between gangs without affecting the general public.
If the general population were armed, the police would also have to be armed leading to an arms race with criminals stemming from the fear of armed confrontation where currently there is no real fear of being killed. As a population in the UK there is no real want or need for relaxation of gun laws. Anyone can own a shotgun and the police firearms officer has to have a reason not to issue one, usually a criminal record or history of mental health issues, obvious red flags. Yet the vast majority wouldnt ever concider applying for a shotgun certificate. Single shot bolt action magazine fed rifles of any calibre or .22 rim fire semi auto are available to anyone who can show good reason for owning one i.e member of a rifle club and have signatures from club chairs supporting your application or pest control with restrictions on what you plan on using for example you wont get a .308 for rat control. A strange difference between USA laws and UK laws is suppressors, where in the UK they are freely available and encouraged as to keep noise disruption down.
Handguns were banned in the UK after the Dunblane massacre https://en.m.wikipedia.org/wiki/Dunblane_massacre which in all honesty was a good decision as despite the illegal holding of guns and import of weapons by gangs from Eastern Europe defenceless children have not been killed by a nutcase by firearm since, something the USA collectively should hang its head in shame about. I understand as a country the USA is too far gone in terms of gun ownership as the cat is out of the bag in terms of being able to control it. However if criminals did not fear getting shot then they wouldnt carry guns and the UK and Europe are living proof of that regarding public saftey.
Gun control in the USA as most posters in here seem to be residents then, probably your only way forward are your current rights with maybe stricter checks on mental health although from what I understand most sales are not retail. Youre in a very fucked situation, a situation I couldnt even begin to think of how to resolve and Id assume neither does anyone else. All I can say with absolute certainty is an armed population does not make you safer despite how it may fee subjectively.
Edit, just a little extra view on the death penalty: I think for certain crimes the death penalty should be concidered although Im of the opinion there are fates worse than death. However, the scary thing about the death penalty and crime is, if you commit a crime where you stand a chance of being put to death what do you have to lose by potentially ending lives that could convict you in the chance you can get away?
Edit 2:Regarding an unarmed population and being able to resist control of the government, in the UK the armed forces swear allegiance to the Queen not any political party largely removing the need for armed insurrection, even so, I have a fair few soldiers as close friends and given orders to turn their weapons on their own country men it just wouldnt happen and the ones that did would rapidly be turned on. Regardless weapons wouldnt stop your financial assets being removed from you by a malevolent government and the united populations weapons would rapidly be turned on each other when it comes to survival.