The confrontation took place on 4 October 1936.
Mosley, who had previously been an MP for the Conservatives and Labour, founded the BUF in 1932. It took inspiration and funding from the Nazi Party in Germany, headed by Adolf Hitler, and the fascist movement in Italy, led by Benito Mussolini.
The BUF styled themselves similarly to a military organisation and became known as the Blackshirts due to their uniform.
On the day, Mosley had been due to give a speech at Shoreditch Town Hall to galvanise support for his far-right message.
He wanted to march his Blackshirts through a predominantly Jewish part of east London as a mark of dominance.
Thousands of Jewish and Irish people, as well as other immigrant communities, turned out to block them – and the Battle of Cable Street unfolded.
It is estimated that about 175 people were injured and some 150 demonstrators were arrested.