As has been said, its the COMM2000 unit (posh name for indicator / wiper stalks and the control unit).
The parts inside wear out.
Its a cheap and easy fix, and you have a couple of options.
1) There's a chap in Bradford who repairs them for around £25. You can either drive to him or send off the part (if you can be without the car for a day or two). He took the time and trouble to identify the parts that wear and had some specially made. Search ebay for "COMM 2000 REPAIR" and his listing should appear. This is my recommendation, I know the guy personally and used his services as a paying customer before.
2) There's a chap in Ellesmere Port who can also do repairs. He's got a few broken ones he's cannibalised for spares.
3) Replace the unit with a new one when Euro Car Parts have their Sale
on. Dealers can charge upto £200 for the unit, depending on what features it has on the stalks, but I've seen them go for as little as £58 during a Sale
. Sadly there are literally dozens of configurations.