David Cameron switched his hair part some time back. BBC ran a story about it that included the Hair Part Theory: http://youtu.be/IarRjZkQJIE
The other Prime Ministers seemed to have stayed the same throughout their careers: Heres a few others:
Margaret Thatcher: left Part
John Major: Right Part
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About John Walter
A long long time ago when I was just 19, I discovered the effects of changing my hair part from right to left. The strength of the change - in my case from a social misfit to "Joe Popular" was amazing, and not only that, when I looked around, it was happening to others.
The Hair Part Theory was the result of researching the effects and putting it into a more scientific framework and language. My sister Catherine Walter was instrumental in getting my vague handwaving theories into a great paper, including a slew of statistics to illustrate just how many leaders we have that are hair parters!
A few years after discovering the Hair Part Theory, I discovered, or more accurately re-discovered a true image mirror - and recognized myself at a deep level. The full story is elsewhere on this blog (link coming), but suffice to say that the True Mirror (the trade name of my perfect version), reflects your hair part the way it actually is, and you can see exactly what you are projecting...it matters!
Hair Part Theory - Discover the Difference! 
In response to the nonsense of parting hair on the right. The idea that it somehow makes you look less confident than it’s counterpart is ridiculous. See Dean Martin and Cary Grant two iconic men of that “50’s” era style. Both of them parted on the right side.
Our understanding of the right part effect is that it is either quite negative, or extremely positive. You can include a host of very well known handsome actors or TV personalities who part on the right. The theory postulates that they already have many positive qualities from being tall and/or handsome. The right part softens them and makes them accessible. There is nothing wrong with the right side – but it is our feeling side, our feminine side. If you don’t have the advantage of being tall and/or handsome, the emphasis on the right side can be offputting.