My information on Thomas Britt and Martha King agree with your records, including birth dates and marriage in Bertie Co., NC. I now note that there is a several year gap between the birth of Thomas’s son Blackman and the rest of his children. The 1850 Johnston Co. census has Martha (don’t know her maiden name) listed as 59 (b. 1791) , therefore it appears that you are correct in assuming that this is not the Martha King that Thomas married in Bertie Co. in 1792, and she is the mother several of Thomas's children.
I have a brother-in-law who is a descendant of Rigdon Britt son of Thomas Britt.