I had been reading that this tour sells out often and to buy tickets in advance. I did buy our tickets for today's tour back in May. The morning tours are continuously sold out - I bet some company like Gate 1 buys them out as it's 50 per tour hour.
At any rate - we arrived at 2:10 for our 3:30 tour (poor distance judging on our first day in Budapest). There's a board in the entry way showing all tickets for sale for the day. All English tours were sold out until 4:30, which didn't seem too bad to me. At 2:10, you could buy tickets for tours in the 4 and 5 o'clock hours.
Same day sales only - if you want to book something further out, you need to do it on their website.