Transavia currently seem to run a lot of bucket and spade routes (PMI, IBZ, AGP) and some popular citybreak places (BCN, PSA). I don't think they do anything what would be classed a traditional business route at the moment. I think they only currently operate 737s - a big challenge for Teesside to fill 3x daily.
KLM would be better selling some slots at LHR - they are doing 10 flights a day (6 x 737, 3 x F70, 1 x E190) - I am staggered that they can make this stack up with the smaller planes. Two of the F70 flights depart 10 minutes from each other!