It's a nightmare - you don't hear from them for weeks and don't have any idea if somethings wrong with the application.
They might even get reduced telephone calls if they bother to update their website
http://www.caa.co.uk/srg/licensing/default.asp giving details of how up-to-date they are with processing.
I sent them an email a few weeks ago and they updated it, but haven't done so again since 21 July.