It's already been living outside in a pot for around 10 years and has survived the harsh recent winters. It's 7ft tall with three massive branches and a thick trunk that almost fills the pot, which has a 2ft diameter. Is it safe to transplant it into the garden, or will it grow to 100ft? It's a tiny London garden, mostly concrete and not much soil space.
Give it a good soak to get it out of the pot and loosen/hack back the roots so you have a smaller rootball. Pop it in a bucket of water and something like Seasol to cheer it up. Dig as deep a hole as you can manage, and wide enough for the rootball. You'll need someone to hold the yucca up while you level it so it doesn't rock, being so heavy. Although they can cope with neglect, they won't say no to bone and meal/chook pellets.
I'd this when the soil warms up a bit.
We had one in our London garden in a west-facing position and it did well. They grow about 10 feet tall in Melbourne, so will probably manage the same. I'm about to hack off a huge off-shoot of my yucca, which is bullying a frangipani. They're unstoppable here.
I'm still pondering what to do. Based on what you've all said, it probably won't take over too much ... but getting it out of the pot and into the ground is going to be a hassle, more so because it will mean digging up a bay tree to make space.
Now, putting the bay tree in the ground was definitely a mistake. It started off as a small herb on my kitchen window sill and has grown into a monster.