It's a real pain and dreadful tactics BUT you need to take a deep breath and work out what's best for you.
It's invariably a tactic by your buyers but you can't rule out that if you say no they'll walk away.
At bottom line, you need to work out whether you can live financially with some price drip and if you can't, you can't and tell them that.
If you lose the buyer and have to remarket, will everyone else in the chain wait for you? They might do up to a point or they might not.
If the buyer pulls out he'll have wasted costs but if that causes the chain to collapse, so will you. If that happens and you need to buy a different house, will that then be more expensive ie outweighing any increase you then get for your house?
It's then down to what negotiating position you think you've got, what you think the buyers actually want (ie is £15k their opening gambit but they'd take less) and how you want to play it. If you call their bluff that might work but if them walking away when there was a compromise, that's not really a great outcome for you.
You also need to know what the timings are : are they saying that if you agree a price drop of some amount that they will exchange today and complete as planned or would then need to get that signed off?
If they'd need to get a price drop signed off then I'd be more tempted to say that if they can't exchange today you'll need to think whether you still want to go ahead.
If they can exchange today, I think I'd be tempted to offer a very small reduction (£2k with perhaps the agent throwing in a small
amount from the commission....) but only on the condition they exchange today. I'd offer it through very gritted teeth but pragmatically that might get you where you
need to be. Or chance it and just say you can't accept that and it needs to happen today.
Personally I wouldn't threaten anything you aren't sure you want to act on.
I wouldn't bother asking for the survey as that implies you're going to consider it and possibly give them the money off.
Good luck....