The rudd also has a distinctly larger eye than the golden shiner, and they're more silvery in the body as opposed to the overall golden colour that this photo displays. Both fish have reddish fins. The rudd has a shorter anal fin, whereas the shiner's anal fin is broader and extends further along toward the tail, as above. Shiners can get to be quite big, it's not uncommon to find one in the 6 inch range. So I still say it's a shiner.
Where was this taken? Shiners are definitely native to the Thames and its tribs, they are not invasives.