It would work with a SCART socket on a TV (at least, the first one; usually AV1 was wired for RGB or composite, and AV2 was composite only or composite and S-VHS); but VCRs don't usually have RGB inputs, only composite.
But there is a simple modification (detailed in the
Advanced User Guide, if my memory serves me well; on early issue motherboards it requires adding a capacitor but later machines have the capacitor already fitted, and a jumper to connect or disconnect it) that will give colour on the BNC output. (It was normally mono-only to prevent colour dot effects from showing up on high-resolution mono monitors.)
If you can get one of the MicroVitec CUB monitors in good condition, that would be the perfect thing to use with it. But they are elderly and probably in need of some TLC.
THOUGHT: Does your Beeb actually give a colour picture on another TV set, when connected via RF? It may be faulty .....