What do you mean by "slow-growing"? The growth habit of bamboos is that a culm appears and grows to its maximum height in one growing season, and thereafter it doesn't grow at all. Some do it in a month, others take a few months. They take a few years for the plant to be able to produce mature culms, but thereafter the culms won't get much bigger, but the plant will spread. "Slow-growing" might mean "slow to reach maturity" or it might mean "slow to spread". Many bamboos are more likely to stay where they are if they are happy than if they are stressed, so many bamboos actually spread more in dry soil. Confine your bamboo within a rhizome barrier about 50cm deep, or a water-filled ditch, if there is any risk of it spreading somewhere you don't want it.

Check out bamboos in the Fargesia genus. They are the main genus of true-clumping bamboos that will grow in cool climates. It includes some smaller cultivars such as Fargesia murieliae "Simba" (about 2m) and F. murieliae "Bimbo" (about 1m). They will of course spread into a tight clump, which will get bigger over time.

The other main genus of true-clumping bamboos for cool climates is Thamnocalamus, and T. crassinodus "Lang Tang" is a modest sized cultivar (about 2-3m).

The popular Black bamboo Phyllostachys nigra (which is actually a form not the species), although technically a running bamboo, is rather slow to mature and spread in typical British conditions. But make sure you don't get one of its truly rampant cousins such as P. nigra "Henonis" (which is actually the true species) or P. nigra "Boryana". Best to buy it from a reputable supplier who will give you a true black bamboo, as there are some poorer forms around.