Thomas Cranmer's First Pray Book of 1549 was not a translation, nor was it taken from the Roman Missal.
The first Prayer Book was a simplification of the Mass in the Sarum
Missal, many of the prayers and rubrics having been omited, and many of the prayers having been penned by Cranmer himself. The Sarum Missal was the version of the Western Liturgy predominantly in use in Britain immediately prior to the unpleasantness of the 16th century. Previously, there had been others, such as the York Missal, Hereford, Bangor &c. There had never been one single western rite, but there were local variants of it, until the Council of Trent of the late 16th cent., which formulated and imposed on the RC Church the Tridentine Mass, which, I believe, is where the Antiochian Liturgy of S. Gregory the Great comes from. ROCOR uses Sarum. More here
Having said that, your point stands as to why there are similarties.