I signed up for this after seeing a story on the BBC News website last October, went to the questionnaire, and the first question indeed used the wording "sex assigned at birth".
So I went to the "withdraw" page and clicked "fully withdraw". To do that you have to phone a number. I did that, and the agent at the other end said my withdrawal would be noted and I would receive a confirmation email. She then asked why. I told her that my sex was observed at birth, no-one assigned it to me, and that a health study that didn't recognise that fact was not based on biology and was therefore not worth taking part in.
Apart from confirmation of my full withdrawal, I have heard nothing since. If the wording is still the same, evidently my comments, and those of others in a similar vein, have been ignored.
And "prefer not to answer"?!!! I mean, given that biological sex has major implications in so many areas of health, what the hell is the point of gathering information on people whose sex you don't know? Spoiler: there is none, the whole exercise is pointless.