As Tiermat said, the CTC clear bag worked for me.
When asked I said that I had let the pressure down, which was true, but just not recently. The additional pressure differential on a low volume bike tire of, say, 15psi max (which it isn't) does not present a risk at all. On a high volume tire (tractor, truck) it could be lethal.
I did fashion a piece of 1/8" ply into a protector for the rear mech, not sure if it was an advantage.
Remember that BA count sports equipment as part of your 23Kg weight allowance so you are unlikely to have to pay extra for luggage, what with hand luggage coming on top. My experience of the application of the rules is that furrin airports are often more strict than the UK. In the UK, I had no problem checking in bike and pannier as the total was under 23Kg. Returning, I was told it was restricted to 1 piece only, so if I checked in the pannier it would cost me. No problem, it turned into hand luggage. With warning I could have kept it on the bike had I chose. Another similar pernickety incident was returning through Bangkok. There, the check in agent whinged because we had two bags, one slightly over, the other under. Cue a couple of moments shifting stuff around, all fine.