The gold cross on the arms is indicative that a direct ancestor served in the Holy Land. The eagle crest indicates that a direct, male line ancestor commanded a ship that was victorious in a sea battle. And the falcons indicate an ancestor served in the crusade under the command of Richard Lionheart. 
It was said that Sir Henry Alexander Webb (1510-1544) established the family for all future time, since to him the coat of arms, was granted. This heraldic ensigna of rank in the New Nobility, that of the thegus, owe their origin in personal service to the prince then reigning. The New Nobility was accordingly one of office due to meritorious service. The device of hereditary coat of armour, a growth of the twelfth century, did much to define and mark out the noble class throughout Europe. When once acquired by grant of the Sovereign, it went on from generation to generation. They who possessed the right of coat of armour formed the class of nobility or gentry. Sir Henry Alexander Webb married Grace Arden, sister of Robert Arden. Mary Webb (Shakespeare's grandmother) married Robert Arden, brother of Grace.
It may be possible to confirm family relationships with Henry by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: