As to 'why are the HFEA so unhappy with them'
No one really knows for sure, but there is definitley some disagreement with reporting their success rates as BFP per cycle (ie taking into account 2 embryos going back) vs BFP per embryo going back (which the HFEA prefer)
The HFEA also hates they do double transfers as standard and refuse to entertain the singleton pregnancy targets they've set.
And lastly, but probably most significantly for you, is the use of off-licence drugs and the 'evidence' base for them.
Dr T and the clinic are clearly unafraid to use off-licence drugs and also share a lot of info with a professor at the Franklin Rosslyn university in Chicago, where much if not most of the thinking of the mechanisms of immunity in fertility have come from.
The university has been instrumental in developing NK testing and also looking at the similarities between NK cells which affect fertility, and immune-based disease such as autoimmune disease, chrons, diabetes etc
Because of this, they started using drugs like Humira and IVIG, and they would argue to great success.
But they have no funding, time or inclination to run big studies, so consider their evidence to be patients like me who have had double-figure failures with other clinics and then get a BFP first time with them after having immune treatment.
Patients think it is wonderful, people like Prof Winston think it is an affront to science, and the HFEA has clearly sided with the latter under the veneer of 'protecting patients from being fleeced'
But as I said upthread, while one round at ARGC cost me nearly £20k, that is a lot less than 10 unsuccessful rounds cost me elsewhere, so I can't see it as bad value in the grand scheme of things