Mark

Very much depends on your FEO, but i would be very surprised if he allows this, on the basis of lower security than inside your house.

Also, i would'nt keep my guns in the garage due to extremes of temperature and humidity.

The security on your garage, (you say it's not able to be opened from outside) is less than that on the house. Ie, no dead locks etc etc.
Also, if it cant be opened from outside...how do you get your car in?
It sounds pedantic i know, but the FEO will think like this.

I reckon the FEO would be very unlikely to let you site it there.

Far better to site it on an exterior wall within the house.
Mine is in our 2nd bedroom, bolted to the outside wall by 6 bolts into the wall and 4 fixings to the floor.

I just had my FEO visit, and he was more than happy.
It aint going anywhere.