An important question Jim.
He may say there is no warranty on a car with such mileage, in which case walk away.
He may say 3 or perhaps 6 months in which case you will have to make a decision.In my view £7.2k for a 240,000 mile car is too much. By way of an example, I have owned from new a 255,000 miles E Class Merc Estate for which WBAC has offered me £155 ! I aint sellin !
The price however has to be one with which you and only you,are comfortable. I am of the view that if you are buying from a Dealer, and it seems that you are, then, regardless of the price you pay in this instance, he is legally responsible under the 2015 Consumer Rights Act, for any significant problem which occurs within 6 months of your purchase. Some Dealers play fair and others don`t.
Do keep us all informed.