I had a similar issue in December with JFK-LHR-CPH where the delay on JFK-LHR messed up my CPH plans and led to my losing a paid hotel night there and my junking the return half of a paid LHR-CPH-LHR I was using to get back to LHR because there was no way we were going to be able to make it to CPH and have any time there at all.

Luckily I did still get EC261 compensation because while I was rerouted the next day JFK-HEL-LHR and stopped there (thus never going to CPH, the “original ticketed point”) the JFK-LHR flight I was originally on was finally canceled after first being delayed.

So if LAX-LHR is canceled and not just delayed you can still stop at LHR and junk all the BUD plans and still get your UK/EC261 compensation for the cancellation