The picture was taken in Branksome Chine, not far from the Tolkiens' bungalow in Lakeside Road, Bournemouth, on 25th May 1971. It was for an article on Tolkien's 80th birthday, and was published in the Sunday Times magazine on 2 January 1972.
(Scull & Hammond; The JRR Tolkien Companion and Guide Vol.I)
The article, written by William Cater, is called 'The Lord of the Hobbits'. This is where the phrase used on the dust-jackets of later editions of LotR comes from: '(For) the English speaking world is divided into those who have read his books _The Hobbit_ and _The Lord of the Rings_ and those who are going to read them'.
Snowdon took some more pictures that day, including the one with Tolkien on the sea shore which is used on the front cover of the paperback ed. of _The Monsters and the Critics and Other Essays_ in 1997.
As for the branksome Chine portrait - I first came across this picture as a poster in my LP of music inspired by LotR, by Bo Hanson (1972).
