BA are pretty good at dealing with baggage damage and will meet reasonable claims but it naturally takes a little time. You may need to buy the replacement for your onward trip before the claim is settled and follow it up later, so take good photographs of the damaged item before you ditch it, to show that it's irreparable and unfit for purpose (i.e not just cosmetic).

BTW you don't need to claim it was damaged in the hold, which is unlikely as well as impossible to prove. Most likely damaged by airport handlers but BA are still responsible for it from check-in at LHR to collection at BKK