I think what you will have to do, is use the drop down box and select a time closest to the time you want, so if you want to eat breakfast at 11am select that and search, you will then be given the times available.
I have just searched for Crystal Palace on the 3rd August for 4 people and it has given me a choice of 10.20am or 11.30am.
I then put in 12.30pm and got this
So there are later dates available you just have to put in the latest time and it will hopefully come up with something you can use.
If not you may have to call up