I would try. The worst they can say is 'no'.
Did you send your application by recorded delivery or special delivery? There's some compensation built into that. Did you include a special delivery return envelope for the return of your documents? This will have bearing on how much compensation you'll get.
As a side note, you'll have a helluva time getting a British passport between now and the 10th, won't you? Is there enough turnaround time?