Actually Cityflyer have been quite successfully nibbling away at BA Heathrow routes, domestic in particular. What started off as an operation aimed at the new financial district at Canary Wharf has progressively taken a good deal of the O&D traffic that formerly went through Heathrow to mainstream Central London, and associated areas. It may come as no surprise that many MPs who used to go through the old efficient T1 domestics heading for their constituencies now turn the other way out of Parliament's front door and head for City.
Part of the reason for the decline in both aircraft size and frequency on Heathrow to GLA/EDI is that quite an amount of this traffic has self-shifted to City, for all its upsides: minimal check in time, ease of access, parking next to the terminal, etc. The "cherry" on the cake is, of course, that Cityflyer have retained proper, complimentary catering. The cabin crew even manage to get round everyone on the flight with it.