Yes, this happened to me eight years ago when we bought our place.
A relatively sought after area - four bids of asking price competing against each other. Was asked for final bids by the end of the next day.
I called a load of local estate agents (not the one selling the property!) and was honest with them and asked for their advice. I figured they didn't have skin in the game and would give me a good steer. One or two didn't want to talk to me but a couple of them said minimum £5k but ideally £10k over asking price given the nature of the market and the area.
I offered £10k + £50 over asking price and won by the £50 as another person offered £10k over. Would recommend doing the same!
If it helps for extra info, once we 'won' the bid, the lender would only value the house at the original asking price and not the offer we had accepted so we had to find this cash ourselves. It was well worth it though as now the house is worth nearly twice what it was.
Good luck.
Cheers.
The thing is - this place has been up for about 3 months, similar time to our flat and we were only able to offer yesterday as we finally got an offer on ours.
When we initially offered, the EA told us they'd let the vendor know but they were pretty confident it would be rejected as they had rejected similar bids over the last few weeks...
That makes me think that they haven't really got loads of offers coming in, perhaps there is only ours and one or two more at best but that they were all 10-15 grand below asking price.
We've now offered 3 grand above asking price and I think that's the highest we'd reasonably be comfortable at. We've already come up 18 grand from our initial offer - our mortgage payments are at the point where we could live fairly comfortably if we got it but would definitely have to start cutting down and saving more.
If we miss out because someone offers more than us then we have to accept it but I feel like we've gone as high as reasonable.