Aviation Hull Insurance would normally cover the whole aircraft including the engines. If a spare engine is fitted (ie one that doesn't belong to the aircraft, be that leased in or originally fitted to another aircraft) then usually the agreed value of the aircraft will be increased to take that into account.
Whilst mechanical failure of the engine is unlikely to be covered, that really only makes reference to the component that failed, the resultant damage would be covered. The issue with engines of course is there will always be betterment when rebuilding it, because some items have to be replaced during strip down and rebuild and others it would be silly to rebuild without refurbing. Thus, the return to full hours will result in an uninsured cost probably equivilent to a full overhaul, it may thus be cheaper not to overhaul but to buy a serivceable second hand engine. BA has the advantage that most of their aircraft are owned, so potentially no lossor will need to be involved in that decision.
Either way, with a reported agreed value of $30m, and a customary Constructive Total Loss amount of 60% of the agreed value, there's not much money to play with since the claim will easily get to $18m. There is always the ability to do some negotiating with the loss adjusters and insurers on all of the numbers except the agreed value and deductible. I am sure IAG will do whatever works best for them, remembering to get another aircraft that will most likely be different (not sure how much spec you can change on the 777, but I know for 737 there's differing avionics, brakes, galleys etc) then have to refit entire cabin to work with BA config, all of which will cost BA several $million it might be worth them just footing some of the bill to get this one flying again for another 6 or 7 years rather than accepting a total loss and be one aircraft down