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Was there any prior negotiations before the agreed price? That can affect responses to further price reduction requests.
Would you feel hard done by if you accept £newasking? If so, was there anything removable in the house you wanted? Then OK we can pay that but we’d insist the thing/s are agreed as part of the sale might yield something.
Or go back with the figure you are happy with and say £figure - waiting to go, it’s a fair price, we can complete on date then hold on to your hats.
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6k is a lot of money but it's nothing in when taking into account everything involved in house buying. The amount you've already spent in legal fees and surveyor costs plus the rent you'll pay whilst trying to find another place (then surveyor and legal fees again) will be far more than the 6k you're trying to save. So yeah, you should ask but if you really want the place then it's probably better to suck up the costs in the long run.
edit - above is me I'm assuming you're in London?
Absolutely - they've been there for ages as well.
To be honest we I was expecting some push back but wanted to make sure that we weren't being awful buyers - are trying to conduct ourselves in good faith, and had gone out of our way to obtain 'fair' quotes for everything - often getting independent reports at our expense, as opposed to people who were quoting to do the work.