The only non-BC race I’m aware of is Thundercross.
You can race all London League races with a day license, so don’t have to be a BC member to participate, but you won’t get any BC points (which only matters if you ride National Trophy races I think, as that is how they grid).
what alternatives are there for racing outside of BC? I know time trials and hill climbs but I'd love to still race MTB or CX