That is such bad news.
What you do next depends on how much the new offer is, how badly you & Clare want it and how much higher you could reasonably go.
Personally, I'd make one more offer (assuming you can afford it) but be prepared to walk away if these b'stards put in another offer.
However, if you cannot afford to go higher under any circs, get your own back and put in a series of higher offers anyway if a bidding war starts. Al least you can then pull out knowing you've got your own back on the gazumper.