People don't really carry handguns around in the UK. If you own a gun in the UK it is most likely a long gun used either as a tool for hunting and pest control or for sport.
The prohibition on transport means you can't take it to the range to shoot.
And where did it say the locked-to-the-car requirement applied only to handguns?
The number of assumptions that you are making here, and appear to be totally unaware of, is staggering.
In the UK, handguns are far more restricted than long arms, and handgun owners are typically required to keep their guns at the range, where they are secured by the range operator when not in use. They are typically only permitted to be used for competitive target shooting, and/or training for such competition.
The vast majority of private vehicular transport of guns is by farmers and other landowners, and occurs over their own private land; Such transport is not subject to the same restrictions as the transport of guns on the public highway.
The majority of guns transported on the public highway are being moved by professionals - gun makers and repairers, land agents, and employees of large estates; In my case, I was working for a gunsmith in Yorkshire, and routinely drove to the Birmingham proof house to have them proofed, reproofed after repair, or certified deactivated.
Private (and licenced) citizens rarely have a need to transport a firearm, but when they do, they must typically only comply with the requirement to take reasonable steps to protect their firearms from theft, and to ensure that they do not cause 'alarm and despondency', which usually means keeping the weapons out of the sight of a casual observer. What is considered 'reasonable' for a private citizen transporting a single shotgun is very different from what is considered reasonable for a gunsmith transporting a large number of guns; The latter should be aware of the higher risk that he might be specifically targeted for theft, and is expected to take the kinds of precautions I outlined above.
It is unlawful to keep a gun for the purpose of self defence (or defence of ones property) in the UK; The question of having a gun accessible for use if needed simply doesn't arise. Indeed, having a gun readily accessible for immediate use in self defence (without a clear reason to have it ready for a legitimate purpose) would, in most circumstances, constitute a crime.
I have (in my capacity as a private licenced gun owner) walked through the centre of Leeds on a busy Saturday, with a shotgun (in a case) over my shoulder - I was involved in a display staged by the Royal Armouries Museum, which included events at two sites about a mile and a half apart. This was perfectly legal, as long as I had a valid shotgun certificate, it wasn't clear to a casual observer that I was carrying a gun, and as long as the gun was unloaded. The rules have certainly changed since then (1989), and as I am no longer in the industry, I have no idea what the current situation is.