The first thing I did was check the wi-fi and card expiry date - both OK. I've tried deleting and rebuying, which didn't work - nothing happening at all - so will try the other solution a bit later. Many thanks.
Tried all the suggestions, but it still stubbornly refused to download. Spent about 40 minutes in online chat with Kindle, attempting various solutions - no use. Was eventually transferred to phone call, when it was fixed in 2 minutes (though without being able to explain why it had happened originally). Many thanks for the advice.