Hi Kay,
Castle Bytham Parish records Reel 816 Sec.1/3 on microfilm.
I only checked from 1803 -1811 but I will look for the later ones next Saturday.These are the ones I found besides Thomas Burchnell which you already have..ie.17 August 1805.
June 7th 1803.
Charlotte daughter of Edward & Elizabeth
March 13th 1807.
Louisa daughter of Francis & Ann
September 21st 1807
William Francis son of William & Elizabeth
March 12th 1809
John Northern son of Francis & Ann (Remarks by vicar Christened,Born & Baptised at Skillington?

)checked with librarian before writing it down as it was so unusual to see it.
November 2nd 1809
Lucretia daughter of William & Elizabeth.
February 12th 1810
Ann daughter of Amy (Bastard)
December 26th 1811
Susanna daughter of William & Elizabeth.
Kathy