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The picture shows no sign of it belonging to one of the Bristol Breweries, so possibly an M & B pub (there were others in Bristol) or a free house. Sorry to be of so little help
Just for your info George, it looks like it was a Fussell's pub (http://breweryhistory.com/wiki/index.php?title=List_of_Sidney_Fussell_%26_Sons_Ltd). The brewery was acquired by Bass, Mitchells & Butlers Ltd in 1962
Thanks for that Rob, and thanks for the link, very interesting site