Britain’s empire did not rest on huge garrisons everywhere

Could Britain simply draw large garrison forces from across the Mediterranean and the wider empire?

No. Britain had few massive overseas garrisons and depended on the Indian Army, Dominion contingents, the BEF, and the deterrent effect of perceived imperial power.

The British Empire did not maintain enough regular troops to occupy every possession through continuous overwhelming force. Its major pools included the British Expeditionary Force, the Indian Army, and Canadian or Australian volunteers rather than innumerable ready garrisons. Imperial control often rested on the perception that Britain could concentrate power when challenged. Gratuitous or abusive uses of force were strategically dangerous because they could give opponents a rallying cause and require still more coercion. In the counterfactual, defending Canada would redirect scarce formations rather than unlock an unlimited imperial reserve.