The train in the first episode consists of Mark 2 coaches, and various electric locomotives, (including a Class 86 in one shot, which is very different from the Class 90 in that it doesn't have a pointed aerodynamic front; but the Class 90 is used in the majority of shots).
Electric trains do not run on the Midland Mainline from London to Sheffield because the line is not electrified, it is operated by Diesel trains, usually an Intercity 125 (sometimes referred to as the HST) which ironically were faster than the Electric train which features in "The Last Train". This switch is supposedly owing to much of the filming taking place on locations around Manchester on the West Coast Mainline.