Checking in to say a big thank you to KJ for starting this thread and for all that info. I now have sports bras that fit and can now do sport without having to keep looking at how embarrassingly my breasts are behaving.
Attempts to find one that fitted in sports shops and bra shops were a waste of time, but thanks to this thread I knew it was worth persisting online. The first one I bought seemed to only fit my smaller breast, but after 3 weeks of correspondence with the seller we concluded that it fitted after all (possibly helped by losing weight at the same time).
The Freya Active core (recommended by an online sports bra specialist) freaked me out at first as it encapsulates to the extent of looking a bit like a 50s/Madonna cone jobbie, but I've got so used to it I am considering using it for everyday wear. It's amazing to feel so supported, like being hugged all day long. And it seems to hold my breasts in a similar position to when I'm standing in a swimming pool. Weird but nice.
After that I ordered some other types because they were on discount. They do the squishing thing which is fine for sport but too 'monoboob' for me to consider wearing it to work prior to the sports class afterwards. Which means I will probably only use those for yoga after all. Then I have more time (and privacy) to get changed before class. I don't mind being seen in my bra, but getting myself into a sports bra takes some doing and rearranging and I am not keen to do that in front of people, especially my work colleagues... Plus it takes a few minutes and that's why I want to wear the bra all day beforehand if possible. I take a normal one for changing into after class.