As a Kenyan native, Barack Obama Sr. was a British subject whose citizenship status was governed by The British Nationality Act of 1948. That same act governed the status of Obama Sr.'s children:
British Nationality Act of 1948 (Part II, Section 5): Subject to the provisions of this section, a person born after the commencement of this Act shall be a citizen of the United Kingdom and Colonies by descent if his father is a citizen of the United Kingdom and Colonies at the time of the birth.
You are missing part of it. ONLY TO LEGITIMATE BIRTHS...of which this was not one as far as we know at this point.
You can find my links about this on a thread with NBC in the title from last week. I am not going to go dig them up again. One is from a UK government site that discusses all of this.
Ann would have had to go to Kenya to have a customary marriage in order for OBama to be a UK citizen if born here..and there later was a law that outlawed such things for births born before 1971 if the party was domiciled in the UK or similiar countries...but I don’t know if they would have taken away his citizenship if he already had it.