Crossley studied 'advanced applied design' at Halifax School of Art, winning a King's Prize. After WWI he worked as a carpet designer before becoming a full time artist in the 1920s.

He was a painter, printmaker and designer, noted for his landscapes and architectural subjects. He also produced scenic watercolours and still lifes in oils. In 1928 he did a series of etchings of Halifax, and provided illustrations for Hanson's Old Inns of Halifax (1933).  After WWII, and in the Spring Exhibition of 1949, he gave his address as Norland, Parc Bean, St Ives. He and his wife both died in St Ives.

In 1962 a Memorial Exhibition was held in Bankfield, nr Halifax, Yorkshire, where he was born and began to show his artistic talents; a further show of his work was held there in 1973.