Well I'm on record saying that anyone who freely chose to use LHR's new terminal has gotten what they deserve. Some people are angry with me, but really it's their own fault. How you could place all your hope and trust in the combined BA/BAA fiasco is beyond me.
So I would book it all on LH or anyone else. Avoid LHR until things improve and they achieve stability in their operations. If you need to go to central London, take the Eurostar from Paris or Brussels.
Of course by the time stability at T5 is achieved, we might be just starting the summer peak season and the hell will begin again. Throw in another labor issue and it will be even worse. I know I sound pessimistic but I have good reason to do so. I may very well use BA in the coming months simply because they are cheaper and the product in the air is quite good, but I would never check bags on BA! And I probably wouldn't fly BA if I absolutely had to be somewhere on time.