Why 6.3 Volts?. In the early 1930s the Americans wanted to make in car radio possible, this also would have helped the military. The standard for car electrics at the time was a 6 Volt lead acid battery, and a freshly charged battery would have had a terminal voltage of 6.3 Volts. As mains transformers could generate any wanted voltage it was decided to standardise on a voltage that would also allow the valve to be heated from a vehicle battery.
6.3 Volts was adopted as the American standard for filaments and heaters in 1934.
The UK standard for mains valves had been 4 Volts, this too can be related to the lead acid battery as two accumulators in series would be 4 Volts. The accumulator used in the home would be run to near exhaustion prior to being taken to the local shop for recharging and therefore for most of its service live would give the 2 Volt terminal voltage associated with the lead acid cell.
In 1937 MOV went American, introducing 6.3V valves with International Octal (IO) base caps.
Mazda's response was to remain staunchly British but to reissue its range of 4V valves with Mazda Octal (MO) base caps, similar to but not interchangeable with IO.
The main move to 6.3V valves for British domestic receivers was essentially a 1940s phenomenon, spurred by the widespread manufacture, importation and use of improved 6.3V American types during WWII.