PAXboy
With a lineage that can be traced directly back to Imperial Airways, I believe that BA is rather more than our "largest" scheduled national carrier.
If you do a vox pox of fellow travellers and ask them who is the UKs flag carrier, I'd be surprised if less than 80% said BA, who generate a tremendous amount of goodwill for this country by providing a consistent level of professional service across a widespread and diverse route network (despite the odd issue)
On the other hand, we do also have......
Virgin (aka Singapore)
bmi (aka Lufty and SAS)
Flybe (short haul only)
easjyJet (short haul only)
All very good airlines, but not quite the same level of prestige IMHO.
So flag carrier status no, but definitely "old money" status around the world and whilst I don't like fuel surcharges, at least they are explicitly stated, so that if the price of oil does ever come down, punters can press for a reduction.