Moving out of cycle lane

Could anyone tell me what the rule is about moving of a solid and broken cycle lane in the UK?

If there is no cycle lane then if I signal to move right across the lane then the car behind has to allow me to move across.  
 

Is this the case if I am in a cycle lane?  Can I signal and move out of the cycle lane and the same rules apply?  I can't find anything in the Highway Code about this. 

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