From looking at the Brill Kids website (http://www.brillbaby.com/teach-baby/baby-swimming.php) I discovered that YouTube had some really good videos on teaching your baby to swim. One in particular proved very useful, as I had been wondering how to move Iona on from being comfortable being submerged to swimming on her own.
When we went swimming today I decided to risk trying to persuade her to float a bit towards the side bar. She was a bit clingy generally, so not too keen, but I was thrilled that, with a hint of support underneath, she managed to "swim" virtually on her own a short distance to the side. Now I have an aim for the next few sessions (not sure how many it will take): to decrease the amount of support until Iona is able to float / swim to the side from a couple of her lengths away.