As an ex-shooter I seriously doubt that it is possible if you wish you remain within the regs as I remember them.
Short of bolting the gun safe to the chassis ? I can't think of any other way.
OK it's getting on a bit on a Saturday evening and maybe a little sherbet is dulling the grey cells so interested to see what others come up with.
Not sure about your local Plod, but up here in Norfolk so long as you take reasonable precautions during transportation no safe is required in a vehicle.
Generally, keep it out of sight, only leave it unattended for a good reason, have the vehicle locked and alarmed (if fitted) and, if possible remove a vital part of the firearm.
If I know I have to leave the vehicle, I always take the bolt, or even complete lower receiver , with me.