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Because they don't want to jump red lights? :)
Well, that's what you get from poor quality traffic schemes--road users don't do what you expect them to do.
I've actually been avoiding Parliament Square because I don't want to see in real life what I've seen in the drawings. It's all shockingly badly designed.
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I tend to use 50% of them - there is one set of Parliament Square lights where it's pointless as you will literally just sit there. The lights for traffic go green and you can perfectly safely proceed in the cycle lane, but the signal is still red for bikes - I use the road here to go around the pointless cycle traffic light and then rejoin the cycle lane to continue. If you stick in the cycle lane it takes several minutes to cover about 200 metres, which is incredibly frustrating and seemingly totally pointless. It's actually this light here in particular (funnily enough green for traffic, red for bikes in this pic): https://goo.gl/maps/M2CFxMJ72vw
This is only coming up from Millbank and getting onto Embankment, totally fine going the other way.
TLDR
What do you expect from the Daily Wail? I somewhat agree though, why aren't cyclists using the lanes?