1: The vehicle is advertised as "Taxed and Tested for... (however long it is)", sold as "Taxed and Tested for... (however long it is)", and that's what you get when you pay for it.
It must, by law, match it's description. So if it was described as 'taxed and tested', then that's what you paid for.
(That's not civil law, BTW... that's a criminal offence.)
2: Any private arrangement the garage have with the previous owner is strictly between them. As a third party you have absolutely no obligation to get involved in it. You are not liable for any payment that somebody else agreed to in a deal you were not involved in.
3: You should have been informed of any deal of this nature up front.
If you settled on an agreed price, and they later come back say they want more - the reason doesn't matter - then tough.
If the price of the vehicle was on display, and the price of this 'extra' payment was not displayed - then they're breaking the law.
4: This is not normal practice, and is therefore suspicious. It should start alarm bells ringing about the honesty of the garage.
I would walk away from this deal if I were you. Cancel all payments and/or ask for your money back. It's your legal right to do so.
There are more serious complaints to the relevant authorities about used-car sales than any other form of transaction in the UK. You don't want to get involved with a dodgy sale.
It's not so much about the £77. But this vendor is not being honest and you don't know what else they've got in store for you.
Hope that helps!