Hi mcdhu,
I can't find the official incident report of BA 9 24 June 1982 but from memory and confirmed by
wikipedia, No 4 engine failed first and the Fire Engine Checklist was completed as far as pulling the FCH and arming the bottles. After the remaining 3 engines had also failed (I guess that would count as "one would have to be in a lot of trouble to even consider relighting a damaged engine"), the first engine to be relit was No 4. Fortunately Flt Engineer Barry Townley-Freeman re-stowed the FCH (not in the QRH relight procedure) - so well done Barry.