I think the connection is:
John Harris married Ann(e) Chelmick 1862 Dec qtr Clun 6a 1097
1871 RG10/2729/42/22 Rhespass, Whitcott, Clun
John Harris head mar 37 Ag Lab b. Bishops Castle
Ann Harris wife 26 b. Clun
John son 7 b. Lydham, Shropshire (1864/5)
Ellenor dau 5 b. Snead, Shropshire
Charles son 2 b. Mainstone, Shropshire
Lucy dau 9 mos b. Mainstone, Shropshire
Ellen Chelmick sister in law single 22 b. Bishops Castle
(Lydham, Snead & Mainstone are all very near B.Castle)
so it would seem that John Harris's mother was a Chelmick.
This is, of course, conjecture and the only way to confirm the connections is by buying the appropriate certificates as and when you can.
Fairlane