Thanks all for these suggestions and comments. It was Peter's suggestion that nailed it. The 6 panels had been connected in parallel. I reconnected them in series (3 lots of 2) as suggested, and now the batteries are charging. @Peter - thanks much!
We may still have problems with the controller - and we may also have batteries of unequal strength (@Jeffrey thanks for that tip). One is new and one not - but both were fully charged at the local charging station before installation. We will keep an eye on them. At the moment I'm just enjoying being able to work the fridge, computer and water pump without the batteries dying.
One more question if I may: Our bulbs are 12v dc and several of them, of course, melted when the 24v system was connected. (I do hope you find this as amusing as my family did). We have now wired the bulbs to *one* of the batteries which is connected in series. Will this yield a 12v supply, or will there still be 24 v coming off the one battery.