score:7
Head to the National Rail station at Terminal 5, find the ticket office (station map; open Monday-Sunday 05:00-23:59), and buy your ticket to Canterbury from there.
(I'm not sure if you can buy the ticket online or not, but personally I'd just buy it from the station.)
Upvote:4
The warning message on National Rail site means, one can only buy tickets online for the trains on national rail network. London underground tickets can not be bought online.
In your search as per the link, journey form London Paddington to London St Pancras is part of London underground. Hence ticket can not be booked.
As Jonik suggested, you can buy tickets from the ticket office at LHR for complete journey instead of booking in advance.