I'm exactly the same way. Health is fine, eat all the right things, don't smoke, and whenever I see a doctor my bp is sky high. Somehow it was OK at Gatwick for my initial Class 1, but the next couple were really high, and my AME told me to get a 24 hour reading before the next one: "If you don't I'll ground you till you do"
Luckily my own GP's surgery has the gizmo to do it, which saved extra cost and hassle. You do know when it's taking it, but you get so used to it, and so fed up with it, that you stop noticing. And my GP said if your bp is OK at night, they tend to assume it's OK.
As it was, mine was within the normal range all day and night, even though I had a stressful work day, losing my temper and getting worried a few times...made little difference to my bp - average overall was about 120/80. Of course next time I went to see my AME it came out sky high again. So now I'm official - White Coat Hypertension - it's down on the form.
That was about two years ago; he hasn't asked me to get another 24 hour reading yet, but I'm fully expecting to have to some day.
Weird thing is, I like my AME, and don't consciously feel tense around him. I guess it's something pretty deeprooted in my case.
Anyway, hope that helps. If you want to know any more about 24 hour readings etc, just ask.