Tunnicliffe was born in 1901 in Langley, Macclesfield, England, the fourth surviving child of William Tunnicliffe (died 20 June 1925) of Lane Ends Farm, Sutton, near Macclesfield, a tenant farmer, formerly a boot and shoemaker, and Margaret (died 21 February 1942). He spent his early years living on the farm at Sutton, where he saw much wildlife. As a young boy he attended Sutton St. James' C.E. Primary School, and in 1916 he began to study at the Macclesfield School of Art. He went on to win a scholarship to the Royal College of Art in London.