This, and just this. No solicitors needed, no engine inspections, no trading standards, no additional time, effort or money required, the car has died within 28 days so will almost certainly be considered not fit for purpose whether you checked the oil or not.
I know people are only trying to help but theres some dodgy advice going on here.
There wasnt until you added some !
The guy has already been contacted by phone and is clearly not going to play ball , for the car to be considered unfit for purpose then someone has to consider it ie a court but it is not cut and dried by any means
The next correct step is a letter stating the issue and how the OP wishes the matter solved , a complete refund is not unreasonable
The car cannot be moved , nor any repair work under gone until authorisation has come back from the seller
I agree that any inspection as to what caused the failure and whether the car was serviced or not is immaterial