Just to be technically correct, BMA operated 700's and the 810 series Viscounts, but not the 'straight' 800, as BEA/BA, KLM etc operated.
I often thought that Vickers would have been better naming the 810 the '900' to distinguish it over and above the 800, as the 810 is a significant improvement over the 800.
Indeed structurally & mechanically there's a bigger jump between the 800 & 810 than there is from the 700 to 800. The 800 is little more than a slightly stretched 700D with rectangular doors - it has the same engines (except the 806), same max T/O & landing weights. The 800 had quite a poor payload/range performance because the max T/O weight wasn't increased from the 700D, thus the extra weight from the fuselage stretch had to come off the payload/fuel, compared to the 700D.
The 810 was vastly improved, with many structural upgrades, control changes & more powerful engines - the quintessential Viscount!