As a purchaser recently, we went slightly over the move in date (1 week). The vendors threatened us with paying the interest, etc etc.
Our delay was not one to suit us, it was a delay with Mortgage protection.
We spoke to our solicitor and he advised that if they served us a Completion notice (which they didn't), after this time, if we could still not close, this did not mean we handed over "interest to them". It meant that they could sue us, and bring us to court. Our solicitor said that we had nothing to worry about. He wrote their solicitor a letter, requesting the threats etc where to stop, etc.
I assume they used this tactic, as they thought we were stalling, but we were as disappointed and anxious to move in, as they were out. Which we explained to their estate agent. One thing I learnt from this whole process is, it can be at times v. stressful, highs and lows from day to day.