Some plants grow or spread ferociously quickly
In a smaller garden can quickly become a problem, so the trick is to avoid getting them in the first place.
Any plant label that says it is fast growing should be avoided. Plants don’t reach puberty and stop at 6ft, if they start growing quickly, they will keep growing quickly;
Some of the worst offenders are:
Russian Vine known as Fallopia – (never buy it)
Virginia Creeper Ok its pretty in Autumn, but not under your eaves, or in your gutters!
Passion Flower it has pretty flowers, but not much else going for it all you end up with is a massive plant, ugly stems and a annual hacking back with mounds of stuff to get rid of for the next 20 years !
Bamboos check if they are clump forming if not then you must contain the roots in a proper bamboo root restrainer or keep it in a pot otherwise they can break into paving and go under buildings.
However some plants also self seed or spread underground pretty rapidly too, this is easier to control as you can either cut the flower spikes before they seed, or you simply pull up the plant wherever it appears where you don’t want it.
However some plants ‘naturalise’ or spread a little too fast too for most smaller gardens;
Allium triquetrum plant 20 and you will have 2000 in 2 years!
Briza Maxima a grass that appears everywhere.
Vinca only use it in the toughest area otherwise it romps away.
Lamium same as the vinca.
If you are blighted by a rampant plant, then best to dig it out and start again, in a small garden it is not worth the hassle trying to keep it tamed and looking pretty, you are unlikely to keep on top of it.