Thanks everyone! I had a trial lesson with a highly recommended teacher who confirmed everything you have all said - the embouchure is the oddest thing!!! I gather you have to channel your inner Thanos with the chin, actually letting my teeth anywhere near the mouthpiece was most peculiar and needed conscious effort. Anyway, the thing I am happiest about is the thing I was most worried about - I have damaged my left wrist and can't hold much weight in that hand, although the fingers still work (waiting for an MRI...) and playing the oboe has been impossible due to the amount of weight (not much, I know) carried by the left thumb. Hey, it doesn't work like that on the saxophone!!!! No weight in the left hand!!!! 2 min in and I was playing it!!!! (Sorry, got a bit excited there, but I've music-less for months and it's been horrible.)
Now I know how to hold it and roughly where to put my fingers and how to make a noise, I am off to try an alto and a tenor. Going to start with a cheapo from Gear 4 Music, give myself 6 months and, if the hand holds up and there's nothing seriously wrong with it, I will look into an upgrade when I have a better idea of where I'm going with it all.
Thanks for all the advice, will give you an update soon...