Sunday to Friday in Berlin might not be too popular, but Friday to Sunday in London is quite attractive. Regardless, I'm not sure that BA are making a serious effort to serve the STN-Berlin market - it's more a glorified ferry to get the aircraft in place for the sunshine flights.
I don't disagree that many want to go to the Canaries for a week, I'm questioning whether it's a market for the well heeled. There are also practical considerations - a round trip to the Canaries takes a while and the aircraft is needed back at LCY on the Sunday too early.