From a recent NXEC email:
To get 20% off, all you need to do is book between 28 September and 2 October, for East Coast travel between 5 October and 20 December.
Terms and conditions
20% discount includes our 10% online discount and applies to our lowest Standard Advance fares only, subject to availability (with limited availability between 23 October to 1 November inclusive). Offer is exclusive to bookings at nationalexpresseastcoast.com/big for travel on National Express East Coast trains only. Bookings must be made by 2 October 2009 inclusive. Standard terms and conditions apply.