If the person already has a face to face appointment, it would be much easier to just ask them their ethnicity at the desk (when they are already verifiying your DOB and sometimes your address). Also, I seem to remember having to state my ethnicity when registering for the Drs anyway. Sending a form out that will hit someone's phone and promptly be deleted or swiped past is not going to yield high return rates. This sounds like they are wanting much more info than just ethnicity.
I sort of agree with Bolton Lad, it is a waste of money the way they are doing it. If they really need the data then they've got to put a bit more effort in. We have done a lot of work on under-served populations and generally you can't really find out who is NOT accessing certain care services, unless you compare the registration/treatment data with the general poulation data. And even then it will be biased towards those who have reported to the local surgery or hospital.
The somewhat sceptical view that "our ethnicity data is not up to a pre-determined standard, GoTo "questionnaire on ethnicity" is probably pretty accurate. My organisation had a similar finding, i.e. all of our employees were caucasian. Next thing you know, every new starter was non-caucasian!