In addition to comments that others have already made, so no point repeating, I'd urge you to cut most of those ...ly adverbs, as they are hard to read, add nothing, and are a sign of amateur writing (no offense intended, I'm not sure how else to express this point). For example, in your first paragraph:
Gerald dropped another lump of sugar into his teacup and stirred it slowly. He stared out of the window over the playing field as rows of young women jerked their arms mechanically up and down and bent their knees energetically. A female teacher stood at the front of the group, her whistle placed in her mouth and her cane swishing time, up and down as the girls bent and straightened and physically jerked their collective way through the routine.
I suggest cutting the words in bold, and see how the flow improves. Arm jerking implies a mechanical movement. The teacher with the whistle and cane makes it clear that the girls are being put through an exercise routine. "Physically" is a nonsense word. How could exercise not be physical?
Every time you feel tempted to write a ...ly adverb, think about what you're trying to achieve with it. Is there a tighter, less lazy way to emphasise the action? Knees pumping is far more visual than knees moving energetically. Someone charging over is more effective than running briskly, and so on.
The only one I'd keep is the shawl being pulled tightly around shoulders, though even then, wrapped tight would read better, I think.