Part exchanged my car but dealer is being incredibly sly and shady

[LesterES]

-I traded in my car on 06/09/2022 for a different one at a dealer
-Made the transaction via debit payment
-They claimed that they did not have the V5C on hand and will therefore send it through the post to me
-Due to this they told me they would tax the car for me as i did not have the V5C to do so however when i got back home it turned out that it was not taxed and i never recieved and email confirmation from the DVLA saying so
-After countless times of being put through to voice mail i finally got through and told me they would email me the invoice yet its been nearly 8 hours since they said this and i recieved nothing
-When trading my car in they did not complete the V5C for transfer of my car to them and instead stated that it would all be fine.
-So overall i left with a car that isnt mine adn is not taxed and would like to know where i stand in legal terms for this situation
I can understand i should have been more thorough when doing the paperwork (or lack of) but it was the first time i had ever traded a car in so wasnt sure to look out for and they took advantage of that

[DE DOGS]

My advice for what its worth, treat every Car salesman / Dealer with suspicion, the endless amounts of complaints we read about, and yet here is another, I am not positive but I think you are able to Tax the car so long as you have Insurance and the Car has a valid MOT, you can check this online. keep on at the dealer until they say he is on the phone again they tend to give in just to get rid of you.