How to assess whether tree roots are causing a problem
I had similar concerns with my home purchase in the U.S. about 7 years ago.  It was noted on my home inspection that A tree had been recently removed (long enough ago for grass to re-grow over the area but there was still a depression) from the front yard where the main lines go.

I had a plumber run a scope down the lines starting at a basement cleanout/drain and inspect the lines all the way to the street to determine if there is any current damage from roots (or anything else).  Cost me an extra $125 but most of that was simply the service call fee (compared to the estimated 10K repairs would have cost, I was happy to pay it).

Of course, this only checks for existing damage.  There is the slimmest of chances that a tree root could be just on the verge of busting through which would have been undetectable but in my case where the tree had already been removed that chance is diminished since tree roots eventually stop growing after the tree is removed.  In your case (with live trees), it would be a higher chance but still unlikely and there really isn't anything else you could do to prevent it that would be cost effective.