Born in 1790, Cleave went to sea and is first documented for his political activities as late as 1828, in London, working to assist Henry Hetherington at the Civil & Religious Association.
A few years later in 1831 Cleave was a printer at Snow Hill in London then at Shoe Lane where he also operated a bookshop and coffee house alongside his printing business.
It was the view of radical publishers that a free press was vital to social, political and moral improvement and that the government were oppressing the people's firmly held beliefs and rights to communicate.
Also in 1836, Cleave joined forces with William Lovett and Henry Hetherington to form the new London Working Men's Association.
In the 1840s as the National Charter Association divided over policy differences and the careers of the early leaders ran their differing courses Cleave sided with the moderate moral force Chartists alongside William Lovett and continued to work for universal suffrage and the complete removal of stamp duty from all newspapers until his death in 1847.