Undelivered SMS is read in an automated voice A work colleague sent me an SMS that I didn't get. Instead an automated voice keeps calling my number and starts reading this message out to me when I answer.

Is this a feature of the iPhone, and if so, how do I turn it off?
I called my service provider but they couldn't do anything.

This call has now been coming every 30 minutes for the last couple of hours and it is really starting to annoy me.

I have set the General/Accessibility/VoiceOver to Off so it's not that.
My carrier, Virgin Mobile, has (had?) a service that would read SMS messages out as a phone call if it believed the destination number was not an SMS-capable cellular phone.

Your colleague's carrier may be doing the same thing.  If you have yet to listen to the entire message, I recommend doing so and seeing if there is an acknowledgement at the end of the call (e.g. "press pound to acknowledge"), which may stop the call.

I bet your problem lies with your colleague's carrier, though.  It is unlikely that either your phone or your own carrier can do much (though the latter may be able to help you block the incoming call.)