You've said you're in the north of the UK, which leaves an obvious candidate because its fully hardy - Fargesia nitida, or Chinese Fountain bamboo. It gets 2.5 to 4 metres tall, and the upper parts of the plant will droop over or cascade once it gets tall enough, which is why its got the common name of Chinese Fountain. Spread is 1 to 1.5 metres, so you can work out from that how many plants you might need for the length of planting area you have.
The only thing is, it doesn't appreciate very strong and cold northerly or easterly winds in winter, nor does it like heavy, waterlogged soil, but this is also true of the majority of bamboos. Fargesia is a clumping bamboo, so you won't find it popping up a couple of metres away, and it doesn't need a root rhizome barrier. Info here https://www.rhs.org.uk/plants/details?plantid=787