If you want it, offer what you think it's worth. If you have a good position financially (i.e. large deposit, could exchange quickly, no chain etc.), make that clear in a written offer.
It is one thing making a cheeky offer on a house that is worth the asking price, something else completely to make a low offer on something that's overpriced.
We offered 45k under asking price for our first house that was on at 265k recently dropped from 295k. The agent didn't even want to put the offer forward. We ended up paying 225k. This year we offered 80k less than asking price on a 450k house, which was accepted, although we withdrew the offer as they had claimed the garden belonged to the house but had a right of way, whereas searches showed that the land was communal. They've put that house back on the market for what we offered.
Our current house, we bought this year when the market was going crazy and we priced up the work that needed doing (kitchen and two bathrooms) and offered 15k less than asking price (asking price was the going rate per square footage for the area in immaculate condition). That is what we bought it at, despite hearing from all the agents we visited with that no one was making offers at the moment.
We make clear how we are calculating our offer when we make it and our position as buyers. So it's clear we have given it a lot of thought and are not just plucking prices out of thin air.
Sometimes, if properties are seriously overpriced, no one makes an offer because they assume it won't be accepted (OH is a former estate agent btw, so he has seen this so often!).
What do you have to lose, really?