Generally, if you were born in England, it's more common to say you were born in England.
Here's a breakdown to help you decide:
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England: If you want to be specific about the actual country within the United Kingdom where you were born, saying "England" is perfectly appropriate and often preferred, especially by English natives.
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UK (United Kingdom): The UK is a broader political entity encompassing England, Scotland, Wales, and Northern Ireland. Saying you were born in the "UK" is accurate, but less specific. It might be more suitable when dealing with international contexts where the distinction between the individual countries isn't as important.
Think of it this way: England is like a state, and the UK is like the country. You could say you were born in California (state) or the United States (country).
Ultimately, the choice is yours, but specifying "England" is often the most natural and informative option for those born there.