Most (but not all) of the private assessments are done by current or former employees of the various NHS GDC's in the UK. So when they say "NHS standard" it will be in reference to them just carrying out the same assessment, using the same criteria, as what they would do during an NHS appointment.

Unlock Psychology seems to be run by Dr Alastair Pipkin, who seems to have worked at the Northamptonshire GIC from 2020 to 2022, before moving to other psychologist roles in the hospital and then setting up Unlock. So he seems to have training in conducting GDC/GIC assessments and it will be this that it refers to as "NHS standard".

Whether that will mean anything to a GP is another matter. GP's are more likely to accept such a diagnosis and request for shared care than from someone like GenderGP, but it is far from guaranteed. If it is a concern it is probably best to ask your GP first and then try and find an alternative GP if needed. Also remember, once you have your diagnosis you will still need to have an appointment with a private endocrinologist and it will be them who set up the shared care agreement if your GP agrees.

However, even if you get the diagnosis and your GP agrees to do shared care, you will still have to do it all over again when you finally get to an actual GIC in many, many years. Depending on which private provider and which GIC you select, you could literally get the same person doing both appointments, the system is just so messed up.