It will be in 1977. The first part of the scheme was the inner suburban services to Welwyn and Hertford, through to the GN&C to Moorgate, opened in 1976 and which cleared many of the suburban trains out of Kings Cross. Once this was done and traffic reduced the track at Kings Cross was completely reorganised and finally electrified, and the outer suburban trains to Royston (only that far, in those days) ran from later in 1977. This was when the eastern of the approach tunnels was abandoned.
The change from loco-hauled to HST main line services also helped ease movements - there used to be a loco stabling point alongside the west side of the station throat, and locos to/from main line trains, especially using the low-numbered platforms on the east side of the station, each had to make multiple Z-shunts right across the layout just to get between the two because of the squashed layout due to the tunnels.
Yes, the electrification trains were made up of former Class 501 units. Over on the West Coast they used converted old LMS carriages instead, and they remained for years afterwards, used for maintenance and for emergency repairs of the overhead.