The original Police Day celebrated the Police confrontation, not with Egyptian protesters, but with the British. As I noted in last year's post:
The Anglo-Egyptian Treaty of 1936 had provided for British withdrawal of its troops from Egypt, except for bases in the Suez Canal Zone for the protection of the Canal, but with the outbreak of the Second World War, Britain had invoked a clause allowing it to reoccupy Egypt. After the war British troops did withdraw to the Canal Zone, but kept force levels well above the 10,000 troops allowed in the treaty. After the Wafd Party, Britain's traditional nationalist rivals, won the 1950 elections, the Egyptian government in October 1951 unilaterally abrogated the treaty and demanded that Britain negotiate for its withdrawal.Let me also rerun that video:
The Cold War was in full swing and Britain (and behind it the US) were already engaged in a struggle with Iranian Prime Minister Mossadeq over Iranian oil, and now faced a challenge to the Suez Canal. The Wafd, and its other traditional rival the King, were both losing influence in Egypt to growing social and economic dissatisfaction and the growth of movements with their own disciplined and sometimes armed militias, including the Muslim Brotherhood, Communists, and others.
The Egyptian government decided to sanction the creation of "Liberation" squads, recruited from vlunteers (many from the Brotherhood), who began a guerrilla war against the British in the Canal Zone. The British responded with proactive moves against the "terrorists," and on January 21 entered Egyptian quarters of Ismailia seeking to uproot the Liberation squads. After coming into conflict with Egyptian police, on the 25 the Lancashire Fusiliers surrounded the Ismailia police headquarters.
The Egyptian Interior Minister, Fuad Seraggedin Pasha (who would survive to head the New Wafd in the 1970s and 1980s), ordered the police in Ismailia to resist the British Army, a dubious decision which, after a six hour siege, left some 50 policemen dead. This video, apparently a British newsreel (there's no sound at least in this version), shows aspects of the British operation, including rounding up prisoners:
The next day, the 26th, was Black Saturday. More on that later today or perhaps Monday.