744, 777, or A318 NYC-LON (biz)?
Having been on all 3 BA aircraft types and as you are looking for as much sleep as possible, the a318 to LCY wins for me. Very comfortable seat and as its aimed more at business travellers, most passengers will also be looking for as much shut-eye as possible. (That's my polite way of saying you are less likely to have children and/or babies in the cabin/on the flight. Pro screaming baby parents, don't shoot me!)