This is just for reference for Mini Cooper One owners (1.6) as I couldn't really find a specific fix on the internet for this error code so hopefully this may help others out in the future who search for this error code and need a solution.
Had the engine warning light come on in the girlfriends Mini Cooper One 1.6 2010. I plugged my OBD2 code reader in and it detected "p0343 Camshaft Position Sensor "A" Circuit High". I suspected it was the camshaft position sensor which was faulty so picked another genuine one up from eurocarparts for around £30. The issue turned out to be this which was good. however I want to point out some of the issues I had and the solutions which may speed up the fix for people and reduce the gray hairs appearing.
I couldn't figure out which sensor was faulty to start with so i used a multi meter to check the voltages. When looking at the connector into the camshaft position sensor from the front with the locking clip on the top the first pin on the left is earth, the middle pin is the signal connection and the pin on the right is the +5v. When checking the signal connection should fluctuate between 2.2v and 2.7v which the faulty sensor didn't. This is how i figured out which was faulty.
The other problem i had was clearing the code. my software requires the code to be cleared with the ignition on but the engine off. With the mini cooper you have a push button start. and having the key in with the engine off doesn't mean the ignition is off I found. This caused me to doubt that the sensor was the fault as the code appeared to keep flagging up. however I cleared the code by starting the car then stalling the engine which then kept the ignition on. This enabled me to clear the code and sort the problem.
The crankshaft sensor Bosch part no. is 419120057
Pictures for referance below. (I grabbed the image from www.pelicanparts.com to indicate the sensors and for refernace)
The intake (inlet) camshaft sensor is located on the left rear of the cylinder head (green arrow). The exhaust (outlet) camshaft sensor is located at the left front of the cylinder head (red arrow)
Hope this helps some people out.
Matt