In the transplanting process:
Double check the drainage, and maybe do some soil preparation. Cordylines aren't fussy, but if you have very poor chalky or sandy soil, now would be a good time to work in some bone meal and seaweed, to feed the roots.
Disturb the roots as little as possible. Cordylines don't get rootbound, so they don't need to have their rootballs broken up like some other trees. If the rootball cracked while removing it from the pot, or a lot of the potting compost fell off in the process, it is a good idea to remove 1/3 to 1/2 of the leaves, starting with oldest ones, to keep the tree from going into shock.
Don't plant too deep. 1/4 inch of the rootball should still be showing when you finish planting it.
Water deeply right after planting, to settle the soil, and collapse any air pockets underground. That would also be a good time to use a root stimulator of some kind.

After planting:
Water more frequently than a mature plant would need--probably next to nothing in the UK!--but only half as often as it needed in the pot. Maybe twice a week for 4-6 weeks, then once a week for the rest of the summer.
Feed lightly after it has been in the ground for a month, to help the roots to grow faster.

Hope this helps to make corrections, Ann!