I am an Indian citizen with both UK and US valid tourist visas.
Can I travel to UK from India to stay for a couple of months and then travel to USA from UK directly without going back to India?
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Your visa is not conditional on your itinerary. You could be arriving from anywhere. There is no requirement to enter from the country where the visa was issued, or from your country of residence, or from any particular country at all.
It's difficult to find information on the internet that confirms this. I suspect that this is because few people think to ask this question.