I use BAA valet parking in T5 every time. The car goes from the upper level to ground floor, with no more than 0.1 miles on the clock. It is kept under cover. On the one occasion I arrived a day late, forgetting to tell them, it wasn’t a problem. Simply paid the extra day at £27 and all sorted. I once booked T5 only to find out my BA flight was leaving from T1. Called them en route and it was switched over with no fuss at all.