Conkers were popular in my patch of London ... don't know if kids still challenge each other with horse chestnuts but it was quite fun: see who had a "Twenty-Twoer" for 22 victories -- probably soaked in vinegar and baked to harden for battle. When I lived in Germany, the Germans thought I was mad picking up horse chestnuts ...
In the late 60s, Airfix kits of airplanes/aeroplanes were popular and we'd have mass formations of kids holding either RAF or Luftwaffe fighters (it seemed the tougher kids had the German planes and would reinforce them with iron filings and thumb tacks) and literally engage in combat ... plastic strewn everywhere afterwards...
Apart from Monopoly, the game "Formula One" caught kids' imagainations hoping to become young Brabhams or Hills.
Since I went to a prep school, the game of "Hic, Haec, Hoc" was very popular -- the American version is "Scissors, Rock, Stone etc." You'd end up with a Chinese burn or slapped wrist for losing the round -- quite a silly game.
Filling out a "Compactum" recording cricket scores must rate with one of the most boring activities for kids ... but budding bankers were clearly earmarked early in life.
Dayboys smuggling candy to boarders probably rated as one of the more interesting activities of 1960s Britain ... many a latter day Spiv found a calling ...

Cheers,
Brian