Hardy Tropicals UK

This is my new Tetrapanax rex. Hope it grows well here in Sunderland.
Are they very invasive or are they easily controlled?

Can be VERY invasive, which is a good thing if you want more plants but you would have to ask your neighbour nicely about collecting suckers that spread under the fence.

I will guarantee in 2 or 3 years your neighbour will start to get some pups coming up. I've already had at least 10 pups so far this year, my plant has been in the ground since 2009 & I now get them coming up upto 6m from it. Having said that it's not a problem in your own garden, they snap off easily & you can pot up any that you want to keep.
(Incidentally it's probably my favorite plant in my garden)

Would root barrier be advised then? as I don't want to cause trouble with neighbours