Which they also rob.
Your argument is flawed at a fundamental level. No matter how heavily you secure the weapon you keep at home, it is still a bigger danger than not having a gun at home in the first place. If you feel that your security precautions mitigate the danger to an acceptable level, so be it. But trying to argue that it doesn't exist at all is rather silly. Especially when I was speaking in general and most people do not take the precautions you take.
Having a large wrench is a bigger danger than not having a large wrench in my home because someone could cave someone's skull in with it (seriously, the thing is massive). I don't see anyone arguing wrenches should be stored at remote sites. Moreover (foreshadowing!), robbery here is relatively uncommon compared to the UK.
It wouldn't be much more expensive to buy your own gun and store it at the range though. In fact, considering the cost of the precautions you have to take at home, it might even end up cheaper.
There are five ranges within 45 minutes of my home. Of those, one - the $30/day range - offers storage, and only of handguns, not rifles. Does me no good. There's also the matter that rifles and shotguns are used for animal/predator control, so even if I were to have some sort of secure storage at some else's site, I need to store it periodically at home before trips into the backcountry when its coming along (as purely a backup to the infinitely more useful bear spray).
The fact that the UK model exists belies the argument that a gun must be kept at home for people to be able to go target shooting. While that may be true in certain cases, it's not certainly not true for a large number of them. As pointed out above, you yourself can't make that argument because it would be fairly easy to make it so that it wasn't a requirement. You have a range within easy reach of your home, your guns could be stored there. If you choose not to do that, that's your choice.
Most ranges here don't offer storage for long guns because storing them
properly in one's home is cheaper, more secure, and more practical. Recall that Canada is a country of 30 million people, and the landmass of the entire UK can fit into any single one of 7 of the Provinces, nevermind the Territories. While the model you propose may be practical and work well in the heavily-urbanized UK, it doesn't here. Canada, like many countries, has a significant firearms culture. While we have reasonable laws that put stringent limits on firearms ownership, storage, and use, an attempt to impose the UK model here would rightly be met with outrage as it doesn't dramatically improve safety while it severely curtails usage and ownership.
In general, while the rate at which firearms are involved in all types of deaths in Canada exceeds that of England and Wales, the homicide rates are fairly similar between the two countries (depending on the year you look at), with Canada's typically being slightly higher. Looking at overall violent crime rate, however, violent crime rates in England and Wales significantly outpace those of Canada (OECD report summarized at
http://www.civitas.org.uk/crime/crime_stats_oecdjan2012.pdf). Would further restrictions on firearms significantly reduce deaths here? Unlikely. The majority of deaths here attributable to firearms are suicides (roughly 75%, varying slightly by year), which is one area where new legislation introduced in the 1990s made little in the way of impact. Moreover, the UK suicide rate overall is actually slightly higher than the Canadian rate, despite the much tighter firearms controls. Accidental deaths attributable to firearms in Canada are quite low, and homicides make up the bulk of the remaining deaths. However, StatsCan data show that the majority of those homicides are committed by unregistered and illegally-owned/stored weapons in the first place. In general, Canada and the UK are quite comparable in terms of crimes and deaths. While Canada has a slightly higher overall homicide rate, the UK has a higher violent crime rate. While firearms are involved in more crimes in Canada, the levels of crime committed in the two countries are quite similar. Most of Canada's gun violence is in suicides; the UK has a barely-higher but almost identical suicide rate to Canada.
In other words, the fact that Canada has far more firearms owners, more firearms in general, and laws permitting more varied uses of them makes almost no real difference when compared to the UK. Why would we apply a model of firearms controls that makes no sense given our geography, legal landscape, and culture when the statistics that control would affect are virtually identical to a country that uses that model anyway?
I don't make this argument, incidentally, when it comes to the United States. That country needs to take a look around and get its collective **** together.
Regardless, I'm not what you'd call a gun-nut, but I do believe in evidence-based policy and legislation, and the evidence generally is that near-bans, like those in the UK, don't have much effect on overall deaths and violence as compared to similar nations with legislation that focus on responsible ownership and use, but this is highly-dependent on the culture and history of the country and a one-size-fits-all-solution does not exist. It's largely cultural. In Canada, we can't fathom the idea of police not being armed with guns; many people in the UK are shocked by the idea of police WITH guns.