The leaves on my container black bamboo have gone brown.

Bamboo, as you may know, is a woodland plant, but alas, in Uk, many do plant it where it will be exposed to the sun. Normally, given the low angle, the sun does not harm the plant, but Uk has this habit of throwing up a sudden week of extremely high temperatures, and whilst it is not the temperature that harms the bamboo, it is the resultant dryness that does the damage.
Unless you have the power of creation, there is little you can do about brown leaves. Remove them, and use as as a mulch around the Bamboo.
Bamboo also like high humidity, so it is good practice to plant adjacent, a water feature. Even a small pot of water will do - anything, so long as you keep it topped up, so that it can condense on the leaves when appropriate conditions prevail (but NOT during winter).
Sogginess is your next aspiration, as most bamboos prolifercate in rain forest locations, and are used to an absolute drenching periodically. So, next year, keep your eye open for drought. As soon as you spot dryness, flood the area with copious amounts of water.
Beware though, bamboo can be invasive, and if you look after it well, it may reward with a take over of all abutting gardens!!!
Lastly, remember that forests deposit their leaves on the ground during the dry seasons, providing an airated mulch that will keep in moisture. This time of year is superb for collecting leaves. Collect alot, and store, for occassional application throughout next year.

Oh yes, and don't forget to give the whole plant a good misting every couple of weeks or so (NOT IN WINTER). It will mimic a very low cloud base, which bamboos love immensely.
Good luck.

Brilliant piece of information Burgundy....thanks very much.....and thanks for asking the question Ming.....I have 3 black stemed bamboos in pots......:>)

Well, lyrical answers are all very well, but....Yes, it will recover - keep it well watered ,and if its been in the same pot for longer than a couple of years, turn it out, split it and repot (preferably in spring) or move the whole thing into a bigger pot. The more the plant grows, the more roots fill the pot, the less soil there is to hold onto moisture for the plant to use. That's all you need to do, apart from a top dressing with something like Growmore in the spring - or a watered on feed like Phostrogen or Miracle Gro general purpose occasionally during the growing season.

Lyrical Bamboo? Well, thanks for the compliment (hugs).