AFAIK that is the design of our system in the UK that civil service/ quangos/ regulators have clearly defined remits, so they can't exceed their power, which would be exactly why they'd need input from someone else, like a judge or panel of judges - which in the UK are probably held in much higher regard than the US, as by default they come across a non-partisan, as would be required to even be inline for such roles, their loyalty being to the law, its history and our democracy, so the CMA referring themselves to the CAT wouldn't look out of place in the UK, and would just look like they got their powers extended by a higher authority, to rubber stamp their take.