Thanks for replying Dazza - turns out the details were right!
The configuration steps I posted in my original article are, in fact, absolutely correct. So if you've got a DrayTek Vigor 2830 or similar device, this is how you can configure it to make use of your multiple static IP addresses without losing your NAT function.
After much perseverance with BT's IT support - who to their credit were very helpful - it turned out that the issue was due to another user having mistyped their username and typed in mine instead, and that user was therefore camping out on my IP range.
Moral of the story: Change your default network password 
Great service from the IT guys though!