Not sure why so much hate towards the op on this one?
You might have 500£ in your account on a particular day waiting on your 6 figure bonus to clear.
Anyway if you agree a price would you pay a penny more especially when they tried to lie about authorisation? Hell NO.
I always take a video of my whole car in the dealer car park when i hand over my keys.
I hope you do take them to court and win, failing that social media the shi! out of them.