Thereis a death in Jul/Aug/Sep 1861 of MArtha Bayram.
This is the same quarter as the birth is registered of Drewery Bayram (age 9 in 1871)
Looks like she dies in childbirth or soon after.
That does pose the question of the mother of all the children born afterMarta's death and before his marriage to MAtilda in 1870.
I think you are right, there was another marriage between the two
Jan /FEb/Mar 1863
Caistor 7a 788
John Bayram, but only one bride and two grooms are listed, so it may be to the one bride Mary Ann Vulture, or it may be to the missing bride!
Whoever she was she died approx 1866- 1870
There are deaths of :
Ann BAyram age 31 in 1870 and Elizabeth Bayram age 28 in 1867, so one of these might be the missing bride. You could get the marriage cert to confirm.