It's not only interline connections where problems can occur if you travel on separate tickets. Buy a BA ticket GLA/LHR and a separate ticket LHR/CDG for example and if BA are late on the first flight they have no obligation to carry you to Paris.
But, as others have said, if it's all on one ticket it is the responsibility of the delivering carrier to get you to your destination. That means if you buy a ticket that says BD GLH/LHR then BA LHR/BKK then KE BKK/SEL and the BD flight is delayed so that you miss BA it is the responsibility of BD to get you to SEL, not just BKK.