I want to have dinner at the Ivy the next time I'm in London, and on their online reservation system only allows you to book one month ahead. But it seems like even one month ahead the last day is booked up unless you want to eat at 22:30

Am I missing something or am I going to have to sit next to a computer at midnight London time one month prior to my trip?

Several years ago, when I arrived in London, I personally went to the restaurant to make the reservation and they were able to accomodate me a few days later.

Do you have a telephone?

Are you staying in a hotel with a concierge?

A good hotel with a good concierge is probably best. Failing that, going by, well-dressed, actually sounds like a useful strategy, particularly the day you want to eat. They hold back tables for celebrities, and if they are short on celebrities, you might get one!

22:30 isn't all that late to eat in London, but you are right about it being booked far in advance.

It is worth persisting.

I got a reservation for Sunday October 5 at 7:00 PM. I tried for Saturday Oct 4, all booked, Friday - all booked, Monday - all booked.

Is the restaurant fairly small or is it just that popular?

The restaurant is both fairly small and that popular.

They also hold back a number of tables for celebrities who want to come at the last minute.

I hope you'll post how the food was. Sometimes places like that are just "eh" but the celebs make it popular.

If you don't mind eating fairly early, you might find that you can get a table if you say that you want to eat pre-theatre.
That way, they know pretty well when your table will be vacated.

Carrybean, No celebrities but the food was really good.

Really? Glad to hear that. I'm sure it wasn't the least expensive meal you had but it's nice you enjoyed it. What did you order?