Toast, Oli and Stealthwolf - my commiserations to you.
If you've a case number then surely a phone call once a week would push things along. Its taken me just under a month to get mine:-
1) went into main dealer with V5 and changed over ownership into my name/address.
2) the day after phoned customer services (0800 0833 914) - spoke to Sarah Ratcliff - who knew all about the plaques. She checked my details which had updated on the computer then created a case number for me to receive my plaque.
3) Voila, 3 weeks later plaque arrives
I cant understand the delay, unless your plaque has already been issued and they'll make new ones as and when they've enough 'orders'.
Also, the Customer Services Manager is called Matthew Young (my letter was from him). Try putting some polite pressure on him to get the ball rolling.
Here's mine: