The BY 737 was probably G-AVRN or RO. RL and RM were also in the fleet, but had lower MGW and probably would not be used on sectors as long as those you mention. The flights ran for several years; I did one as an F/O in 1980, and they had been running for a few years before that.
Crews were not exactly specially chosen; my recollection is that Captains needed to do a clearance flight with a trainer before operating in command. There were some ex military pilots who were excluded because they were prohibited by MoD from entering Soviet territory.
Albert has the right name for your Captain.