Each ticket is a separate contract. You will have to complete each contract and check in again. If you miss a flight you have invalidated your contract and you will have to buy a new ticket or at least upgrade/change your existing ticket. Using the normal connection times is therefore inadvisable.
Hmmm.
Booked a holiday through BA with flights from my local airport to LAX. All flights with BA but they've ticketed each sector separately, I've been assuming that I'd be able to through check our bags, is this not the case?