We've located the source of the problem, which was the Content Delivery Network (CDN) that we use. We haven't been able to idenitify what the exact cause was or why some people were affected and not others, so we've decided to move to a different CDN provider altogether. Hopefully this should have resolved the issues for everybody and things should now be working OK. Sorry to anyone who was affected by this.
John
To me it's fixed, thank you very much!