If they refuse get advice for your local Trading Standards (or the Trading Standards that covers the area where the garage is).

You have clearly been mis sold the car and if it went to court the judgement would go in your favour. But be aware, that does not necessarily mean theywould refund you, many dodgy garages change their name etc and pretend they do not know anything about the previous owner. It can be a long process involving Bayliffs to get the money.

Hopefully they will simply pay up.

If the deposit was on a Credit Card contact your provider immediately, they are legally required to assist.

I would appreciate some advice... I've certainly learned a lesson but I'm hoping to get the money back if possible.

I think you have been misled by the seller, but that may not mean the car is a bad 'un, if you agreed to a noticeably low price. The car may have suffered a minor accident and been professionally repaired - presumably you didn't notice any obvious damage or mismatched paintwork ?

My own car suffered minor front-end damage at 8 years old, enough for my insurers to write it off. I drove it home after the bump and the local bodyshop did the repair after I 'bought it back' from the insurers. There's no visible damage and it drives just the same.

Of course most people will not like the idea of a car which isn't 'perfect', but that may be only an emotional objection, rather than a practical one. Did this Jazz look suspiciously cheap ?

The fact that the Number plate was not readily shown is not good as you have discovered

Cat N is not recorded on the log book and the damage for a cat N can be very minor

The advertised price of the car should be some 20% less than its equivalent good car and if its not big money you are spending it could be a good buy but I suspect you have lost all trust with the seller which is understandable