I thought I'd share my research into the English branch of the Allen family.
I descend from Arthur Allen's brother Roger.
I have evidence that Arthur Allen's mother was Margery Woodhouse, not Margaret King. The marriage licence of John Allen of Droitwich and Margery Woodhouse of Salwarpe appears in "Calendar of Wills and Administration in the Constitory Court of the Bishop of Worcester", which also includes marriage bonds during that time, dating to 1594.
The wills of William Woodhouse of Salwarpe (1603) and Richard Woodhouse (1606) mentions John Allen, described, respectively, as son-in-law and brother (that is brother-in-law) (note: the latter calls him his 'brother Allen', but I have little doubt it is the same man, especially since William Woodhouse also mentions his son Richard in his 1603 will.
The connection to the Woodhouse family is further confirmed by the will of the John Allen, the son of Roger Allen (and nephew to Arthur Allen), dating to 1696, in which he mentions his kinsman John French. John French was the son of Richard French and Alice Woodhouse, both of Salwarpe; Alice Woodhouse was the niece of Margery Woodhouse
I hope that some find this of interest.