Born in Grimsby, the artist began his studies in art at the early age of twelve years. His three mentors included Stanhope FORBES, with whom he studied between c1886-8 (exact time uncertain) whilst living in Lamorna, which he later memorialized by naming his first Lincolnshire home 'Lamorna'.

Subsequently, he undertook further study with Frank BRANGWYN and J M Swan at the Stratford Road studio in Kensington, London. In the 1901 Census he is listed with the occupation of Fish Merchant, it being a large family business, although family information suggests that he was (perhaps also) a partner in a cabinet-making company.

Jennison initially married Letitia Hollingworth (m 1895-1918), and then Elsie Grace Clifton, with two children born of each union. Regarded in art circles as specialising in oil portraits of civic dignitaries, he also painted still-life and landscape in watercolour. Some works remain within the family, including one painting I wish... painted with an accompanying poem for his young niece. He was a member of the Usher Art Gallery (Lincoln) Hanging Committee in 1933, and exhibited latterly at Liverpool and in county exhibitions around Lincolnshire.