Turns out that they prefer the sweet tastes of biscuits and even bananas etc to broccoli and carrots.
They'll whinge and whine about being hungry, so you offer them some peas or avocado or something and they will literally push it out of the way, look you straight in the eye, and tell you about how hungry they are (...but not hungry enough to eat the veggies in front of them!). Offer them crisps or biscuits or even just fruity-yoghurt and they'll scoff it down super-fast because presumably it tastes nicer.
Can't blame them really.