I think sub 12 air rifle hunting is of critical importance to the UK and have no doubt it can be performed humanely and ethically.
Anyone who has the slightest understanding of the environment, ecology and economy of this country knows certain species have to be controlled, and anyone who understands shooting knows that small calibre powder burners and shotguns are not suitable for shooting small quarry in many instances. The alternative to air rifles is poison and traps which are nether 100% species specific or as humane/lethal as shooting.

First I think we have to look at the compounded successful effects that many decades of sub 12 air rifle hunting has had on the UK, so imagine if all the quarry taken by sub 12 hunting over many decades had been allowed to live and reproduce, and consider how damaging that would have been on the environment, ecology and economy of the UK.
If sub 12 hunting was banned we would either be up to our ankles in rats, the red squirrels and songbirds would disappear and vast amounts of crops would be destroyed, alternatively the mass use of poison and traps would destroy much the very wild life we desperately need to preserve.

Secondly, for me proof of humane and ethical hunting with sub 12 air rifles comes down to one thing and that is my shot/kill ratio, I haven't hunted for a while now but when I was very actively hunting I was getting a 95% shot/kill which is a minimum of 19 out of 20 shots at quarry would kill the quarry. Obviously I didn't start hunting with this kind of success (my first hunting trip nearly put me off hunting for life), for me to achieve this I had to work very hard (theory and practical) on three main areas -
Markmanship
Fieldcraft
Quarry behaviour knowledge

Personally if I couldn't achieve over a 90% shot/kill ratio I'd stop hunting for a while until I figured out where I was going wrong and try not to resort to blaming the tools I was using for the job. I realised biggest weaknesses when I started hunting were not knowing angled shots, judging the wind incorrectly, shooting too far and not waiting until the quarry had settled before taking a shot, once I got these aspects sorted hunting became a pleasure because of the effectiveness of each shot and knowing of the greater good I was doing.