It usually applies to later flowering perennials that form a clump and throw up lots of stems-so works for asters, phlox and such like -it gives you a stockier multi-stemmed plant that flowers slightly later that if you hadn't cut it back.
Bit like pinching out on bedding plants gives you side shoots
But doesn't work on all plants and and aaquilegia isn't that sort of plant
I chelsea chop sedums, but I only do half the stems. I was once told that you can completely cut back aquilegias when they have finished flowering, but I thought that this was to tidy them up.
It is. I cut back the flower stems, but leave the leaves - I prefer to know where they are!
It's worth leaving some of them to go to seed if you want them to set seed and produce new plants.
Aquilegias are already in flower or have even finished by Chelsea so are too early for the chop to work.
The purpose of the chop is to delay flowering completely or in part to spread the season of flowering. It also encourages plants such as sedums to produce shorter, stockier growth which doesn't flop and straggle. Works on phlox, lysimachia and other later flowering plants.