I am seeing very cheap tickets from San Jose, CA to London (new direct flight), but for some reason tickets that connect in London are very expensive. But if I buy separate BA tickets (for example SJC - LHR, LHR - NCE), it's more reasonable.

What is the missed connection policy on BA if I do this? I read that if I connect from an AA flight to a BA flight on a different ticket that they'll protect you with a missed connection. But does this apply to two BA tickets?