He received his education first at a school kept by Mr. Creaton of Billesdon, and then under Charles Berry, minister of the Great Meeting at Leicester.
He soon became an able leader-writer, and for more than thirty years wrote nearly all the leading articles of the Leicester Chronicle, the chief liberal paper in Leicestershire, which had belonged to his father since 1813.
He worked actively for the abolition of the corn laws and of church rates, and for the extension of the electoral franchise.
In 1847, in conjunction with William Kelly, he arranged the ancient manuscripts which were lying in a state of disorder in the Leicester corporation muniment-room.
The manuscripts of the ancient merchant guild of Leicester gave him a mass of original materials for this book, which is referred to by John Richard Green and other writers (cf.
Thompson was one of the founders of the Leicestershire Architectural and Archæological Society in 1855, and to its Transactions he contributed numerous papers and communications.