After I traveled abroad, my Mac thinks I'm in the wrong timezone I have selected the option to set the time zone base on my current location. It correctly detects my location (London), but it still keeps the time as New York time.

See screenshot image.

This is OSX 10.9.5 Macbook Pro
I think you have to move the physical time zone marker to your location, I had to do that to reset my times one from California to New York.