You can take your chance on a seat being available, but it is much easier to order and book them ahead, by telephone or internet. You will be given a code number which you then enter in a machine at Waterloo, which then prints your ticket. If you prefer, you can queue and give the number to a human who will also print your ticket.
Thanks for the answers. I found the Eurostar website, and a single ticket to Belgium without advance booking costs a ludicrous ₤149. I ended up flying to Stuttgart, and even with a hotel in Stuttgart due to late arrival and rail travel to where I wanted to go in Germany, it was still cheaper than this.