The other possible line to follow is that the car should be as described. As Martin says above, if the buyer asked about the car being a write-off and got a lie as an answer, that is grounds to reject the car. But establishing this could be very difficult and may come down to one person's word against another's.

This, from Autotrader's website, may make uncomfortable reading for the OP:

"Buying from a private seller means you’re not covered by any specific laws other than those relating to the legal right to sell goods. As such, it’s important to make thorough checks.

At the very least, you should:
• Expect the car to be sold as described by the seller
• Ensure the seller has the legal right to sell the car
• Get the seller’s landline telephone number and home address
• Prepare a receipt and ensure both you and the seller keep a copy

You should always carry out a vehicle history check to ensure the car hasn’t been written-off, recorded as stolen or subject to outstanding finance before you commit to buying a car." (Italics mine)

To be perfectly honest it makes little difference to its value at this age.

By the sound of it, it was recently written off. A scratched bumper can easily write off a car of this age and no one is going to carry out a major repair on it as the figures don't add up.

The vendor should have told you but if it is otherwise sound and decent it isn't the end of the world.

You need to make an appointment with your local VOSA office for the check and, once carried out, they will issue the V5.