LONDON—British health minister Matt Hancock quit on Saturday after he was caught breaking COVID-19 rules by kissing and embracing an aide in his office, enraging colleagues and the public who have been living under lockdown. In the latest scandal to rock a government that has overseen one of the highest death tolls from the coronavirus pandemic, Hancock, 42, wrote to Prime Minister Boris Johnson to resign, saying he had let people down. Since The Sun newspaper published photos on Friday of the married minister embracing a woman whom he had appointed to a taxpayer-funded role to scrutinize the performance of his department, an increasing number of his fellow Conservative lawmakers had privately called for him to go. Hancock has been at the center of the government’s fight against the pandemic, routinely appearing on television to tell people to follow strict rules and to defend his department against criticism of its …