Phil,
Another couple protected by the remarkable crashworthiness of a Morgan. Very glad you and you partner are shaken but not broken.
As others have said, a reputable insurance company will used the selling price for a comparable car from dealers in your area. You could find that you actually get more for your car than you paid for it!
I have one experience of dealing with a write-off, my sons Renault Clio in 2009. It was insured by Aviva and the process was painless. We got a cheque that allowed Andy to replace it like for like and because he wasn't at fault (he was rammed in the back whilst stationary) there was no excess to pay and he didn't lose any No Claims Bonus.
Since then he has had no further accidents, but the whiplash injury took about 5 years to fully fade away.
He now drives a Focus ST for fun and a Mazda 6 for work.
You should be back in a Morgan before long.