I think you are correct. Amazing considering how little I could find on Briton AFTER your answer.
Oddly, the German Wikipedia page had more photos
https://de.wikipedia.org/wiki/Briton_Motor_Company
I posted this in another forum, and someone pointed out that I had missed the propeller in front of the radiator cap!
Further research into the travels of the individuals in the car discount the possibility of 1909 in USA (which is consistent with a later Briton), as the driver did not move to the USA until 1913, and the gentleman on rear passenger side visited Europe in Summer of 1909, later Winter of 1911 (wrong season for picture) and Summer of 1913. The other two passengers resided in Germany (but had visited the USA in 1909, hence the confusion).
The driver is a Dutchman, and the license plate, while not very clear, appears consistent with the Dutch system then in use.
So its a very good chance to be a 1912-1913 Briton, with the photo taken in Summer 1913.
THANK YOU.