I have never heard any suggestion of using the .303 Browning in the ground role. It would have required various accessories, as already mentioned, and probably also a special supply of belted .303 ammo (the Vickers used a different belt).
Finally, it would have faced limitations on its use because of its high RoF of 1,200 rpm, which did not meet the British Army’s philosophy and would have required frequent breaks for cooling down. I don’t think the gun had the kind of quick-change barrel that the MG 34 and 42 had.
The .30 Brownings used in British AFVs were the same as the US ones, in .30-06 calibre, and fired at the normal rate of c.500 rpm.