If LHR isn't to get a third runway (which it isn't in the forseeable future) there is only room for one operator on domestic routes. With one operator you may well need regulation. The trouble is that EU (& UK) aviation policy is geated around encouraging competition which requires enough infrastructure. My view is that a monopoly operator could be forced to handle transfer traffic for competitors, although IAG would doubtless say that the same should happen at FRA, CDG, AMS, etc.
Some routes such as Cairo, Moscow & Saudi Arabia could make sense for VS. As part of the BA/VS tie up slots had to be surrendered (to DL) to provide competition on the BOS & MIA routes - although DL has just dropped one of the BOS frequencies. The same could happen here - I certainly can't see the transfer being allowed to go ahead without some surrender of slots.
I doubt that VS has the financial or mangement resources to take over bmi.