Buying a Eurostar ticket

We bought tickets a few weeks ago for a July date. We checked at about midnight London time but they weren't available. We checked an hour later and they still weren't available. At about 3 AM their time we were able to buy tickets. I don't know if this matters but we are traveling from Paris to London (one hour difference between these 2 cities). FWIW It is easier to land midweek low priced tickets vs weekend tickets.

You can buy them any time. It is not like a concert where you have to buy tickets within a matter of hours. There are many departures a day and it is pretty unlikely that the least expensive seats would sell out on the first day. I'm assuming you are buying from eurostar.com.

Right now on the U.S site http://www.eurostar.com/us-en, I see tickets available through Sept 15 and the least expensive tickets are $54.

In our case I wanted to buy the tickets on the day they became available because we wanted a specific time of day and there are 6 of us wanting to sit together--parents, children and grandparents. On our midweek date in July there are still low priced tickets but on Friday of that week there is only the first train if the day with the lowest priced tickets still available. I also noticed on the man in seat 61 site there are very few clustered seats around a table for our fare category and since a couple of people in our group don't handle riding backwards I wanted one of the limited forward/backwards seating clusters. We were kind of picky, I'll admit, for booking on the day the tickets became available...

I don't think it is that critical to book on the first day. Bookings open 180 days (6 months) before departure, but people don't rush out and buy on the first day, most people looking for cheap seats about 3 months in advance.

There is one train per hour to Paris (approx 18 trains per day full timetable here), each train has 10 coaches, 750 seats: 206 in first class, 544 in standard class. According to my arithmetic that is 13500 seats per day (9792 2nd class). That number of sets will not sell out fast, no matter how specific your requirements are.

Eurostar tickets are available for booking on an earlier basis than many other rail tickets. That is only really an issue if you want to connect with another rail operator. You can by add-ons at the UK end direct from Eurostar which can be cheaper than those available from the companies themselves, and have connection protection.