Not just British, it was a global effort and a global boycott. The British government of the time wasn't a supporter of Mandela.

> I am sure Hitler was going to prefer that other countries don't report on what was happening so that he can continue to eliminate all German Jews.

The Holocaust was barely reported at the time. Much of the details were only discovered by horrified Allied troops that overran the camps. Internment and the other racial discriminatory laws were reported; and the wave of Jewish refugees was, along with the high levels of opposition to taking in refugees.

Some of those have very striking parallels today.