British Nationality could be obtained through your birth, or through the birth of any one of your parents or grandparents, in Iraq. This arises because of Britain's relationship with Iraq and Britain's Colonial history.
To determine what form of British Nationality you might have, an analysis of your family's history must be done, and then applying it to the Nationality laws of Iraq that have been passed over the years.
STATUS OF IRAQ
Between 27.09.1924 and 02.10.1932, Iraq was a British Mandated Territory.
Since that date and up to the present day, it is considered an independent foreign country.
For more information on how British Nationality could be gained through your birth (or a parent's birth) in a British Mandated Territory coupled with a UK-born grandparent, watch this short video by Philip Gamble: