OK, I believe the match is good and can go ahead in the direction proposed.
There is actually a very unusual situation which gave me pause.
Millicent de Bickering/Bekering was married first to John Burdon and by him had a sole daughter and heir Elizabeth Burdon. This Elizabeth Burdon married Robert Markham, son of the Judge John Markham in question.
Apparently in an effort to get control of all of the Burdon estates Judge John Markham married Millicent (Bickering) Burdon, e.g. his own son’s mother-in-law.
Go down to John’s son Robert Markham-66, to his wife Elizabeth Burden-30, and then her mother Millicent Bickering-1, you will find another Millicent which needs to be merged.
So, Millicent UNKNOWN-3067, Millicent Bickering-1 and Millicent Berkeryng-2 are all the same person. I would probably merge them into Bickering-1. Preferred LNAB being either Bickering or Bekering.
See: History of Parliament: Nicholas Burdon