Cut Price Durham Filling Station Advice

If a class 142 DMU (2 car set) train was filled with a full tank of Diesel would it get to Durham from London?
If it left London kings-cross on a full tank of Diesel would it reach Durham station before needing a re-fuel traveling on the East coast mainline.
Thank you for your answers.
I would not fancy the ride with a maximum top speed of only 75 MPH.
Not to worry.