Under British rule, a settlement grew at the narrow point in the river where cattle crossed, known as Wacca Pilatka to the Seminole and the Cow Ford to the British.

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Which one is correct?
1. Under British rule
2. Under the British rule
3. Under a British rule

#1

less commonly, #2
never #3

The correct phrase in this context is option 1: "Under British rule."

The correct phrase in this context would be "Under British rule." This phrase indicates that the settlement was under the authority and governance of the British.