charleski, thank you very much! I went all through the InDesign documents and removed the spaces, replacing them with underscores. And then it had a problem with using inverted commas in titles although it hadn't flagged that up previously! So I got rid of the inverted commas, exported without fonts embedded, and it worked!!!!!
Good to see my first ePub in an iPhone.
One thing though, internal and external links in ePubs don't seem to work in the iPhone, although they worked in ADE. Is this usually the case? (Maybe a question for another thread)