Under British rule, the practice was initially tolerated. In the province of Bengal, sati was attended by a colonial government official, which states historian A.F. Salahuddin Ahmed, "not only seemed to accord an official sanction, but also increased its prestige value". Between 1815 and 1818, the number of sati in Bengal province doubled from 378 to 839. Under sustained campaigning against sati by Christian missionaries such as William Carey and Brahmin Hindu reformers such as Ram Mohan Roy, the provincial government banned sati in 1829. This was followed up by similar laws by the authorities in the princely states of India in the ensuing decades, with a general ban for the whole of India issued by Queen Victoria in 1861. In Nepal, sati was banned in 1920. The Indian Sati Prevention Act from 1988 further criminalised any type of aiding, abetting, and glorifying of sati.

Based on this passage, who had spearheaded the movement against the tradition of sati? Let's give stream of consciousness first:
The relevant information to answer the above question is: Under sustained campaigning against sati by Christian missionaries such as William Carey and Brahmin Hindu reformers such as Ram Mohan Roy, the provincial government banned sati in 1829.
So, the final answer is Christian missionaries such as William Carey and Brahmin Hindu reformers such as Ram Mohan Roy.