How wonderfully preposterous getting a doctor's note to certify that someone is rather tall and will be cramped in economy.

Fortunately, sometimes mere common sense rather than ticking boxes ("Has a medical note?") prevails. Our company has a silly policy than only MDs get to use Business Premier on Eurostar. Others can use J on long-haul travel and First on other trains, but in Eurostar are confined to economy. I, a humble ED, simply do not fit in economy - Eurostar economy has much less legroom than many trains and planes. My PA simply asked me to print and sign a statement to this effect, and lo and behold (after a sign-off by some bean-counter somewhere) a Business Premier ticket was procured. And no doctor's time was wasted.