The period of time during which Brown published his problems is known as The Transition School which was between 1845 and 1862. Noted problemist H.G.M. Weenink (1892-1931) described the period as being of the utmost importance in the history of the development of the chess problem.
When in 1845 Howard Staunton published Reverend Loveday's Indian Theme problem the imagination of problemists was fired and they began inventing all kinds of themes. In the world of chess problems it was gradually recognized that aesthetically it was desirable to have problems without unnecessary moves. In other words, it was considered inartistic to take six or seven moves to show a theme if it could be done in two or three. Nowadays problems are almost all either mates in two or three moves. Longer mates are generally avoided unless the theme requires it.
Over half of Brown's problems were published in Howard Staunton’s column in the Illustrated London News. Today most of his problems would be considered as pretty ordinary, but, as mentioned, in the 1850s the idea of what made a good problem was not so sophisticated.
Back in those days descendents of respectable families (Brown's father was a bookseller) did not have much choice of careers, so Brown, born into a family of staunch Methodists, trained as a minister.
In England the Wesleyan Methodist Church was the name used by a movement following its split from the Church of England after the death of John Wesley. Wesleyan was added to their title to differentiate them from the Welsh Calvinistic Methodists, founded by George Whitefield who, like Wesley and his brother Charles, had been a member of the Holy Club in Oxford to which the originally derogatory epithet "Methodist" was first applied and from the Primitive Methodist movement, which had separated from the Wesleyans in 1807.
The Wesleyan Methodist Church, like the Wesley brothers, held to Arminian theology rather than Whitefield's Calvinism. Brown's family were supporters of the Wesleyan movement and in 1847 Brown was considered a fit person to study for the ministry.
After three years of study, he entered the Theological Institute where he continued his studies for another three years. However, after serving just one year as a Methodist minister, he resigned and became a member of the Anglican Church.
In 1863 he took employment as a coal merchant's clerk and lived in Kentish Town, a section of London. It was during this time that his interest in chess composition became a reality and publication of his studies appeared in various chess columns, including Staunton's.
Shortly after his death from tuberculosis at the age of 36, Chess Strategy, a collection of his compositions, believed to have been complied at the insistence of Staunton, was published as a memorial to his work and to help his destitute family.
I don't normally publish problems, but here's one of Brown's that I liked. It's a two mover, but it also contains mates in 3 and 4 moves as well as two mates in 5 moves. I don't think it was ever intended to be anything other than a mate in two problem though.