It goes beyond that.
To this very day he has a right (whether he has every claimed it directly or not) to be a British Citizen. And as such the UK could apply their laws to him should be physically within their bounderies.
Obama is STILL a dual Citizen!
He was born a Brit. He did not lose that right when Kenya gained independence in 1963. He merely gained the opportunity to obtain Kenya citizenship - as well! But that did NOT nullify his access to British citizenship. In fact to formally nullify you need a specific form filled out - form RN from the British government.
From a college professor:
http://instruct.westvalley.edu/hannigan/Eligibility_Dialogue.pdf
"Therefore the President seems to hold dual citizenship with Great Briton and the United States."
"The KC article 95 confirms the status of Commonwealth status to its Kenyan citizens. No Act, law or decree therefore removed Barak‘s Commonwealth Citizenship status as received when he received Kenyan Citizenship."