They might not be crashing but they may be busting airspace.
and the statistical evidence for the above claim is... exactly where?
Prejudices die hard.
I have read various UK stats in the past and could never see this.
Yes there are some TAAs doing busts but not any significant figure.
Human factors can always make it possible. I busted a piece of the LTMA near Farnborough, for some 20-30 seconds, as a result of talking to a passenger and forgetting to descend under the next stepdown (4400ft to 3400ft or whatever). One solution to that is to fly the whole lot at 2400ft but then you increase the risk of a mid-air, which at > 3000ft is very much lower.
There are other ways for "serious" pilots for busting CAS. For example the old chestnut of flying from France to the UK, where you were nicely cruising along at FL100 (on a Eurocontrol IFR flight plan) and the French handed you over to "London 124.6". Those born and bred in Brigh'on will know that 124.6 means their IFR clearance has just been unilaterally and quietly destroyed and now (in breach of ICAO) they are
VFR traffic but a foreigner will just carry on. London Info have radar (though they are not allowed to say so) so if you call them up in good time they will tell you to descend below FL075 (etc) but if you delay, or the handover occurs later, you will bust the Worthing CTA. Not that there is any CAT in there at FL100 that far out over water, but a bust is a bust.
This went on for years... because the only French unit with a "handover deal" with London
Control was Paris
Control, and PC didn't do traffic below FL120, so to continue your IFR clearance you had to be on oxygen
Much more recently, this issue has been somewhat fixed. I have had a handover from Brest to LC (from Cherbourg) at FL090, and been handled by PC at FL100 and handed over to LC at FL100. So evidently some heads were banged together, but this is relevant if reading old CAS bust stats as a large % of these will be well equipped planes.
On page 65 "largely as a result of overuse of GPS" should read "largely as a result of over reliance on GPS"
I don't think they have evidence for either.
Remember the AAIB gets involved only in
crashes, and ask yourself how the over-use of a GPS can cause a crash.
You would have to be fiddling with knobs all the way through a spiral dive into the ground. I'd love to know how they established the cause there
Or mis-program a GPS and do a CFIT, but these are very rare in the UK. The hallmark of a CFIT due to a basic nav c0ckup is a long straight line into a hill, but that isn't a GPS issue; it is caused by a shortage of obstacle clearance

You can do a CFIT while VOR tracking just as well, and hundreds if not thousands have done over the decades, around the world.
So I think the statement is just simple bollocks.