What is the eventual height and what root system do Cordyline Australis have?

Cordylines like these have a ball-like root that will ultimately spread out as far as your foliage. So if the foliage is touching your house..... Remember the footings will be about a foot beyond the walls.

Problems with roots appear when plants absorb too much water from the soil under the footings and the foundations are not strong enough to withstand the resulting movement. But this is not such a problem with cordylines.

I should think the tall one is pretty near its limit for the UK.

Thank you so much for taking the time to reply to my query. I feel much happier about the Cordylines now.
Anne.