Sell off BACon ? Well here are the financial options.
1. Sell to another airline (a "trade sale"). Difficult for BA because any other such airline is likely to be a competitor.
2. Sell to management. This is a euphemism for "Sell to mangement who have borrowed millions from financiers". And the financiers invariably want their money back, plus plus plus, in the medium term (typically about 4-5 years). And who would be in the market then ? See 1. above.
3. Sell to Venture Capitalists. Just a more open version of 2. above, with the same end result.
What is the value of BACon ? Typically it's the real value of the assets if you sold them on the secondhand market, often not much if the aircraft are leased, plus about 3-5 times annual profits, which we all believe is diddly squat, less any reorganisation costs like staff reductions. So there's not a lot in it for BA. Remember BA buying Dan-Air for £1 ?
From a purely financial perspective the best route which would maximise BA's revenue would be to franchise it out, preferably in sections rather than one chunk. This would be a complete going-back on the past decade in this area and lead to all sorts of "Grand Old Duke of York" comparisons. But it would give BA the best financial return.
By the way, have you ever seen the loads on BA out of LCY (especially midday), the routes abandoned, or the lack of subsequent expansion on the routes still operating ? It's not a gold mine.