I think I was confusing the The National Gallery (UK) with The National Portrait Gallery (UK)in my Posting. However, there is a portrait of 'James Brindley' at : http://www.npg.org.uk/live/index.asphttp://www.npg.org.uk/live/index.asp
I found his portrait after searching the collection. Put his name in the box marked 'sitter' You should reach his portrait( number NPG 6170) by Francis Parsons C 1770. (James lived 1716 - 1772.) The reproduction of the painting is small, and even after clicking on it to enlarge it, its still not easy to see.
Keri, The James Brindley I am referring to is the English 18th Engineer. You may already know of these 'Brindley' links, but if not, there is some info here. I hope this is of some help or interest to you :-))