I've done BA48 many times into LHR and I usually manage to make it into the Arrivals lounge before the breakfast clears. They used to clear at 12.00 but for the past few years they leave the hot food out until at least 12.30. As for immigration I think fast track is now open until 1.00 so that should help speed things up assuming your eligible to use it. The UK/EU line is usually fairly quick no more than 10-15mins.