Can they? I think it would be just as quick flying to LHR and jumping on the Heathrow Express to Paddington and then getting a cab to the east end of London and probably for the same price considering that City Star are not that cheap!
Remember that ABZ-LCY has been done in the past with a British European 146 and then Scot Airways tried it using a D328. Both companies packed it in due to poor loads/yields. That was before bmi started operating ABZ-LHR and now with their low cost model that mainline has adopted it is now even cheaper to get to LHR!
ABZ-LBA is a waste of time since the loads barely fill a J32 with Eastern except on peak times e.g. Friday evening. LBA-LCY loads seem to a questionable with bmi but they have not really advertised the route so that might explain that!