This is wooly aphid or mealy bug. It lodges right down where the leaves separate. Whilst there are several chemicals on sale you will need to use several times as even with chemicals it it a difficult pest to kill. Try parting the leaves gently and dislodge with a soft brush soaked in the chemical before giving it a drench.

Unfortunately, malathion was the only effective treatment for Phormium Mealy Bug, and its been withdrawn, I think at least 2 years ago. Even with that, though, it needed treating every spring.
Provado Ultimate Bug Killer ready to use spray is supposed to be the most effective treatment available today - and as Jimmy above says, it really needs to be applied by pulling apart the leaves at the base as far as possible, and getting the treatment inside there. You do not need to spray the whole plant, the bug lives inside the third or quarter of the leaves nearest the base.

Try rubbing alcohol (surgical spirit) and soap. Mix straight rubbing alcohol (no water), and 1/2 a teaspoon of Simple soap. The soap works to break down the waxy coating, and the rubbing alcohol will dehydrate the mealy bugs, killing them. Again it is necessary to repeat the treatment once a week until eradicated and as Bamboo says, to prevent the little sweeties reappearing, treat every year.

Hello,

Thank you very much for your responding to my post and for the advice you have given me.

I will be giving it my best and see if I save the plants left.