I've just started my very own (owned! yay!)garden and have an enormous rubber plant--well tree: say, 8-10 metres--in the back garden. I love it, but the neighbours said it has, in the past, wriggled its roots into their sewage pipes so that they had to have them all replaced. Yikes! Does anyone know about the invasiveness of these trees? I really don't want to get rid of it, and if it's going to take another 20 years before it's naughty again, maybe I'll take my chances...

There are thousands on plants around much better than that. Get Rid of it I say

Around our area you are not permitted to grow those invasive plants.