I sure they vendor of the new place will accept. They will be in the same position in you in that they don't want to loose out on a sale (assuming they don't have multiple people offering). If they do, you'll just have to suck it and cover the costs another way if possible, or not sell yours. Tell them the revised offer is too low, and you've had someone else offering full asking price on yours (which you might not have), but say you like them and are willing to hold on. Perhaps 217.5k?
Come to think of it, when I sold the above place a few days before exchange they came back and said they wanted 5k off because they found some damp.
I said no and that I had taken 20k off the asking price as it was so they could take it or leave it. The sale went ahead I think he was just trying his luck.