Offering on a house?

[What2Offer]

We saw a house we love yesterday and are trying to figure out what to offer, all advice appreciated!

• House is on the market at 460k
• Has been on since last April/May
• Was originally put up at 480k, but reduced to 460k first week in Jan.
• it's currently rented out short term, as the family moved out in the summer

460k is over our budget, we were originally looking at properties around the 400k mark but it's a fab house so we'd be willing to stretch ourselves (a bit!).
Our position is that we've sold our house but can't sign contracts until we have an onward purchase, so are very serious and ready to buy.
So, what do we offer? Friends have said as low as 15% under, which is way too low I think (391k). I don't want to piss the seller off, but at the same time realise I need to get it for the best price for me.
All advice appreciated!

Clarify your position first, do you mean you have an offer on your house or has the conveyancing been done and you’re in a position to exchange contracts as soon as you’ve found one to buy? As a former EA it’s frustrating when people say they’ve sold their house, but they mean they have an offer. Also be clear on your position in regard to mortgage, you have a MIP? What percentage loan is it? All these are factors in what makes a good offer. If you’re in a good place ie. conveyancing done and low percentage loan I’d go to £410 expecting it to be turned down and try to settle a bit higher say £430.

What have others in similar condition and size gone for since it went up for sale? They'll want to get what others have got surely.

Thanks, that's very helpful.
It's a one off, so nothing really to compare it to. Although I will do a bit more investigating on what's sold in the area recently.
We've accepted an offer, all the conveyancing (legal stuff, right?) is done for our sale. We lost the house we we're going to buy, so are back house hunting again. But I don't want to lose my sale, so need to move quickly.

Also have approval in principle for mortgage, that's all sorted.