going back to my mother in law when she sold her house in london everything was going through fine usual pace 2months + !! when within days of exchange the purchasers solicitor started whinging about an asbestos shed in the garden.Now bearing in mind they had the surveyers report within days of putting the offer in nothing was said until right at the last moment.Mother in law ended up knocking £2,000 of the price.
If it had been down to me i would have stood my ground called there bluff and threatened to put the house back on the market you have to remember the purchaser would have spent £££s on various fees which they would lose if it had been put back on the market.
Just dont be intimidated by threats and certainly dont let them think you are desperate to move.