I suppose the attitude is that flood plains are fine so long as they're on someone else's land?

In times past, a short flood was welcomed because of the fine silt left behind however, since then, so many houses have been built (in the wrong places?) and so much more land has been metalled one way or another that there's far more surface water being quickly directed in to water courses.

Sooooo, you've a few choices. 1/ put up with the flooding, 2/ deepen the water courses where the flooding's causing trouble or 3/ make some new watercourses.

3/ is not possible? Of course it is, look at the new London Tideway.

I'm familiar with gabions and thinking about where some were used on the Clywedog, if they're not properly used, yes, what you mentioned will happen. In the case I'm thinking of, the river simply undermined them (they weren't taken deep enough in to the ground) and eventually the river changed course. The Clywedog isn't a big river, in times when the river's low, in places you could carefully walk over it in shoes BUT..... don't go anywhere near it in flood!