Beetroot
With care — Allowed by some hospitals and not others, or allowed only prepared a particular way.
In one line: Peel it and cook it until completely soft, then purée it or sieve it. Never grate it raw.

Beetroot is a root vegetable, and root vegetables peeled and cooked soft are the backbone of the vegetable side of this diet. There is nothing structurally unusual about it. The skin is tough and comes off, the flesh cooks down like swede or carrot, and blended it makes one of the smoothest soups you can put in a bowl.
The preparation
Peeled, cooked until completely soft, then puréed or sieved. Boil or roast whole and peel afterwards if you prefer, which keeps more of the colour, but check that a knife goes in with no resistance before it comes out of the pot. Never grated raw, which is how beetroot most often appears and is the one form that is out.
Pickled beetroot is a different thing and is not used here, since pickles are on the avoid list.
Where hospitals differ
Beetroot is not named on the leaflet this book follows. It is treated in this book as a peeled root vegetable cooked soft, on the same footing as carrot and swede, which is how St George's handles root vegetables generally.
If you have been told to leave it out
Carrot and potato make the same soup in a different colour, and the method is identical. Swede and carrot cooked together and blended with a little cream give a sweeter version with no claim attached to it at all.