There were no burials in Higham for Rawlins or variants between 1538 - 1702.
But, there was an entry for:
8 Mar 1647 for John Reyner
30 Apr 1657 for Liddiah Reyner, daughter of the widow
One source for James Rawlins says that he took cloth from London to Mr. Reyner of York and another that he paid a rate for Mr. Rayner's provision, 1661 and 1662.