Without knowing the route it's difficult to give specific information so I guess you just want general pointers. BA can rebook you on many other airlines if it is a short notice cancellation (under 24 hours). If you elect to do something else then BA are within their rights not to refund that. You do need to call up to protect the onward connection. It can be ressurected in LHR if necessary but it's painful and you may simply be told to call the Contact Centre anyway.