Oranges and Lemons was sung and played very often in the Grainger household from the mid-1940's to the early-1950's both at children's' parties and in our sing-songs. My mother, Peggy Grainger, learned it herself in her own childhood in the playground at St. George's School, Worcester in the early-1920's.
As a game, two components were needed, to whit a two-person arch (one person would be the orange and the other the lemon: usually the parents or older children) they rest of the company making a ring and passing under the arch while singing "Oranges and Lemons". When the singing finished, marked by the line "I do not know", said the Great Bell of Bow" , chanting then started. During the chant, the arch would make chopping motions with their arms and when the chant stopped, the unfortunate child whose head was "chopped-off" by the arch would be invited to join the arch either as an orange or as a lemon. Thereupon the victim would leave the ring and put its arms around the waist of its chosen fruit tree. This would continue until all members of the ring had their heads chopped-off, and thus the game finished with everybody with their arms around each others' waists and as a Grande Finale, a tug-of-war would take place with everyone falling down on the floor. Great stuff!
Peggy Grainger's version can be found in A Mum's (Mostly Musical) Memories.

Sung: by the ring
"Oranges and lemons", says the bells of St. Clement's.
"When will you pay me?", says the bells of Old Bailey.
"When I get rich", says the bells of Shoreditch.
"When will that be?", says the bells of Stepney.
"I do not know", says the Great Bell of Bow.

Spoken: by the arch
Here comes the candle to light you to bed.
Here comes the chopper to chop of your head.
Chip, chop, on the block goes the last man's head!

Whispered: by the victim
Either "oranges" or "lemons".