Hello Geraint,
You are suffering from post-purchase blues - quite a normal reaction. Regrettably, in your situation, I think your concerns are valid.
Did you check the on-line MOT history of the car before you even went to look at, or particularly before committing to buy it?
Checking it now, probably explains the reasons for its juddering - severely worn CV joint boot, rough wheel bearing, welded wheel/s, brakes imbalance, worn suspension pins, tyre worn below limit - I could go on.
I notice the car passed its latest MOT, now advisory-free a week or so ago, and my guess is you bought it from a dealer who arranged a new MOT before sale.
Geraint:- PLEASE DO NOT DRIVE THIS CAR AT SPEED AND WITH ENTHUSIASM UNTIL IT HAS BEEN PROPERLY ASSESSED. ( apologies for caps.) This car has used some printer ink in its MOT history!
Way forward:- if you bought it from a dealer then e-mail them ( you need a written record) and explain its juddering at speed , and it appears to be overheating, and you intend to book it in with an MOT station of your choice to check the car out.
If you bought it privately, let us know the wording of the advert.
Regards,
Gareth.