It's reassuring to know that I'm not the only ukulele player to have a problem holding the thing well. With a guitar, you sit and support it on your knee, or use a strap when standing - but a ukulele is so small that it's not so straightforward. The neck can slip alarmingly when changing certain chords. But I am not alone with this problem, and I've seen the Uke Leash recommended on the Ukulele Underground Forum. At the Uke group yesterday, most people were using a strap of a similar design - a strap from the neck of the uke to a loop that goes over the opposite arm and sits round the shoulder. It simply stops the uke from slipping down. You can easily make a strap like this, but I want one that will unclip from the peghead - so I've ordered one. They have to come from America, but that's okay - I've had no problems with deliveries from the States.
So - I expect it may take a couple of weeks - we'll see! And then I'll review it. Watch this space!