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I am not for one second saying don't check. And I totally agree that looking can negate the need to indicate. But I do think indicating clearly is a damn good idea, and I also know that on a normal road with one lane in each direction indicating right does give an driver behind you an obligation not to overtake. If you can see the oncoming road is clear, and you indicate clearly then wait a few seconds, then if everyone on the road is doing what they should you are safe to turn right without looking because it is a breach of the highway code to overtake a road user indicating right. Bad idea because being right is not much use if you're dead.
Changing lanes is different as I don't believe that you have any right to change lanes ever unless you have checked it is safe to do so - but we were talking about a right turn I thought.
The signal is an expression of intent to change vector, but does not grant the right to do so. For example when changing lane to just signal and then swerve into the lane would be ignorant/stupid/dangerous. There could be a driver who is driving with due care and attention and at an appropriate speed, just changing into the lane they are in would be to cause an accident. If this happened it would be unlikely that the driver would be found to be at fault. In exactly the same manner as someone driving along and just signalling and swerving into a different lane would be at fault, so would your hypothetical cyclist.
I would suggest it is the other way right round. Adequate checking and eye contact with drivers behind me often gets drivers to allow me to change into their lane, without me needing to signal.