Dave, watch it - EI leave from Gates 85 and 86 at LHR, IIRC..the furthest Gates from the Lounges (having done it on my honeymoon trip) and EI is notorious for being late (both of our flights LHR/DUB and DUB/LHR were late - the latter was 2.5 hours late).
I'd second
aura's suggestion..I'd only fly BA - although you won't get auto-op upped to WT+ anymore