Ultimatums

I have made an offer on a property of the asking price but do not want to go much above this amount. I am considering contacing the estate agent and telling them that my offer stands until e.g. 1pm today.

Has anyone ever tried this, and has it been successful or what response have you gotten back?

It's quite normal and common to do this.
If the EA has been trying to sell property fo the last 10 years , he will certainly agree, otherwise if property "new" on the market, he will certainly reject .Hard to know what the feedback from EA will be. There are many other parameters that need to be considered....
Give it a shot, and you will see.