He was born in Plymouth, November 14, 1847. From his earliest youth he was fond of Dartmoor, his early associations centring around the neighbourhood of Sheepstor, Walkhampton, Meavy, and Yannadon. He acquired a taste for antiquities from his mother. Later on, Crossing explored Tavistock, Coryton, Lydford, Okehampton, and the northern borders of the Moor, as well as South Brent, on its southern verge.

After leaving school at Plymouth, he went to the Independent College at Taunton, and then returned to finish his education at the Mannamead School (Later called Plymouth College).

His earliest literary efforts were in the direction of fiction - 'thrilling romances,' composed for the delectation of his school-fellows. His first essay in poetry was at the age of fourteen, when a poem written by him appeared in the pages of Young England, December, 1861.

In 1863 he went for a short coastal voyage to Wales, and gained a liking for the sea; and in 1864 he joined a vessel bound for Canada, and had a narrow escape, nearly being crushed by an iceberg during the night. Returning from this voyage, he took to business pursuits in Plymouth, and then recommenced his Dartmoor explorations.

In 1872 he married and settled down at South Brent. In the previous year he began making notes about his rambles, without, however, any systematic arrangement; after his marriage he seems to have become more methodical, and to have decided to write a book descriptive of the moorland district. In the 1890s he published numerous other works and his Guide to Dartmoor, illustrated by Philip Guy Stevens in 1909. He was much afflicted by rheumatism in the last 25 years of his life and in 1921 his wife died. From July 1925 to his death Crossing was an invalid and he died at Plymouth, 3 September 1928.

He is now considered one of the best authorities on Dartmoor and its antiquities, having made it the subject of his life's work. He was one of the earliest members of the Dartmoor Preservation Association, joining it immediately on its formation. It is quite probable that he effectively started the popularity of the modern pursuit of letterboxing. In his book Guide to Dartmoor he refers to what is likely to have been the first letter box. It was placed at Cranmere Pool on northern Dartmoor by a local guide in 1854. In Crossing's memory in 1938 a plaque and letterbox were placed at Duck's Pool on the southern moor by some individuals and members of a walking club known as Dobson's Moormen. He was buried with his wife at Mary Tavy: his house at Mary Tavy bears a commemorative tablet unveiled in 1952.

The style of Crossing's work in Guide to Dartmoor has similarities to the much more recent work of Alfred Wainwright. The hand drawn sketches of views and rough maps of walks together with the descriptive nature of the walks are like those of the Wainwright guides to the Lake District (see Lakeland Guides).