I was in a similar situation recently - found the house I loved and started with a bid 25K under the AP on the very next day after the first open viewing. (It was the second identical house on that block I had bid on through the same agent, so she already knew about me.)
Agent said that vendor wanted to wait, so I said I could pay 12.5K under the AP if vendor was willing to take it off the market there and then (it was not actual bid, mind you!). The vendor said he would only consider taking it off the market at 15K over the AP. (What's the AP for if vendor won't even be willing to sell at that price, I thought then?)
A few weeks passed and the vendor saw reason. Someone had (according to the EA) put down an offer for 2.5K more than our previous offer at 20K under, but in the end we closed at 5K under the AP.
We are now sale agreed and the contracts should be signed in July.
Why am I telling you this? Well, it was exactly the house we wanted in the street we wanted, and there are not many of those! So we really wanted it, and the agent knew that.
This was both an advantage and a disadvantage - the EA knew we would not want to lose the house and would be prepared to pay more, but she also knew that we were serious buyers. So if you really want that house, be prepared to pay a little bit more than someone who only bought it for an investment would. After all, you'll recoup the extra cost in the enjoyment of living in a place you really love.