The first record I found of this photograph is in Oxford Figures: Eight Centuries of the Mathematical Sciences. Professor Michael Atiyah shares some recollections of J.H.C. Whitehead and his pigs:
See also an interview with Atiyah at Oxford Mathematics Interviews. (Whitehead and pigs enter at the two-minute mark.)
This might explain why Whitehead liked pigs:
• Henry Whitehead, whose school of topology attracted scholars from around the world, was a keen pig farmer: he claimed to derive mathematical inspiration by scratching his pigs’ backs for an hour every afternoon.
source: Oxford Mathematical Institute Spring Newsletter