Looking at the actual figures for the LGW route, ASW are probably hurting but Flybe seem to be coming off worse.
8183 pax travelled in total. Even if every single one flew with BE, that only gives them 46 pax per flight, 59% LF. Not good. A more realistic figure is the 56% that they state - 4583 - which gives 25.7 pax per flight/33% LF - ouch!
That figure is given credibility by the amount it would leave for ASW - 3600, or 14.5 per flight. This compares with 21.63 in 2008 (a drop of 32%). Plymouth is down 18% on 2008, so if we presume that would have been replicated in NQY the actual hit on ASW's numbers by BE is also an 18% reduction. The overall LF for ASW into LGW is 64.3%, so while not great is much better than Flybe. Of course, the normal disclaimer applies: we don't know the yield. However, for BE in particular this is unlikely to be great.
On the basis of the figures above, even if BE were to drive ASW away completely, the numbers don't seem to be there for them to make a go of the route long term, not outside of summer anyway.