Storing spare tube under saddle bag The saddle bag I own has two elastic loops on the underside.
From reading this question on long-term storage of tubes I can see tubes don't like changing temperatures (not really a problem in Ireland as the temperature doesn't vary too drastically) or direct sunlight.
If I were to wrap the tube (to protect from the elements and sunlight), would under the saddle bag be a suitable place to store it? At the moment I keep it inside the saddle bag but I would like to have the extra bit of space if at all possible.
I only cycle ~100km per week and it's a cheap spare tube so it's easily replaceable. (Doesn't need to offer long-term protection).
I'll sum up some of the comments with some concerns that you need to address:


Excessive moisture
Temperature changes
Abrasion and movement
Access


Simply wrapping the tube in something non/semi-porous and opaque will help keep it safe from the elements, but not from temperature changes, but it sounds like that's not going to be too much of a factor. You should also consider any bits of dirt, water, road, mud that are going to be kicked up from your rear wheel under the saddle bag. This could cause some excessive wear after you installed the tube in the tire unless you clean it first.

As a few of the other comments have stated, you may want to consider other means of storing your ride supplies. You've got a spare tube but do you have a pump? Is it a frame pump or small enough to store in a bag? Tire levers and a multitool are also going to take up space. I'd recommend looking at either a larger bag or purchasing something like a hydration pack (CamelBak, Dakine, Osprey, etc.) to store your tools, clothes, food, and whatever else. That way you can plan a variety of rides without needing to awkwardly stow tubes, pumps, and anything else on your bike!

EDIT: (Kudos to Chris H) If you've already got a way of storing all that,you want to make sure it is secure and protected from dirt. It doesn't need to be sealed completely, as you want to make sure any moisture such as condensation can evaporate.