How close? Is the wall high, old, new?

They will grow out of chimneys in deserted factories without the chimneys falling down (well not at first anyway!)if this is any encouragement.
No need to ask four times!

I think the problem is Stera that it is not clear whether a question has gone through or not when you press the button. I've been confused myself sometimes.

30-40cm away and you will have no problem. Buddlejas have tiny root masses compared to their summer top-growth and,in soil, the roots are quite lazy. I would advise you to prune the plant every April to ensure it never becomes huge, although even then the danger is wind-rock and collapse more than root invasion.

I don't entirely agree, Buddlejagarden - I had to move one that had only been planted for around 18 months a few years back, and it had roots which extended up to 7/8 feet which were a good inch thick, mostly along the surface, with one or two fairly deep roots. So whilst generally, I don't think buddleia will be a threat to a wall with decent footings, if its a low wall without proper footings, and its planted only 6 inches away, that would be another matter. So the question, without more information, is a bit like asking how long is a piece of string...

There's a mature one planted right up close against our garden wall (on the outside) that's been there for at least 15 years with no sign of any damage.

Honeysuckle,that's true - easily done.