Barnes Family Link to Jamaica?:

Last year I received an email from Alan Eyre, a Research Fellow at the University of the West Indies. The content of the email is shown below.
Dear Mike,  
I am just about completing a biography of Dr. Isaac Edmestone Barnes, C.M., C.E., FRGS, (1857-c. 1930), a renowned Jamaican scientist.   He appears to be descended from a (?) Dereyk Barnes (his first name is almost illegible in the documents, and has to be guessed).  All we know about this Barnes is that he came from somewhere in Britain, possibly with Oliver Cromwell's army that captured Jamaica in 1655, and that in 1682 he acquired (purchased or received in lieu of wages) 400 acres of land in Jamaica which he named Friendship. There are hundreds of descendants of this Barnes all over Jamaica today, including the Anglo-Caribbean footballer John Barnes.   Any possible clues?
At the moment I am unable to say whether there is a link to our branch of the Barnes family, as my research into the family has so far not reached the period of the English Civil War (1642-1651) - I am still roughly a generation away. However, it is interesting to speculate if any of our family did fight in the Civil War and if so, on which side - Royalist or Roundhead?