Flybe, on behalf of SN, used to fly a Dash into LHR not that long ago. They did it for about a year or so in 2012-2013 I seem to remember. It may even make the odd appearance, but I think SN now only use the A319/20 and Avro.
Still, LHR-EDI doesn't seem to fit much into their product, but time will tell. They might be better trying to link other regional airports to LHR, for example, DND, CWL, JER, GCI, IOM, MME even NWI and HUY and getting a few interline agreements on the go to feed markets BA and others dont and which are not that easy to transfer to from LHR and are otherwise cumbersome and lenghty by road or rail. That would make them a real UK regional carrier, offering feeder services to a main hub, rather than the mix and match network they have now which is mostly just point to point traffic.