I am reading Democracy in Europe: A History by Luciano Canfora. In his short section on the English Civil War he states
There is another element in the Levellers' thinking that should also be taken into account: their reference to the "native* factor. During the second day at Putney, Henry Ireton, Cromwell's brother-in-law, argued that before William the Conqueror the Anglo-Saxons had a very ancient constitution based upon liberty and equality. The "inherent rights" of the English were inherited from this "constitution", and had been crushed under the rule of the Norman Kings until the reign of Charles I. Thanks to Ireton's elementary dialectic, this vision of England's distant and recent history led to the blocking of the radicals' demand for true universal suffrage. This ambiguity came from the phrase uttered by the Levellers' exponent himself: "We believe that all people who have not compromised their inherent right should have an equal vote in elections." The expression"inherent right", coupled with the theory of Anglo-Saxons' ancient liberty, was used as grounds for the argument that, in any case, not all members of the community were necessarily equal with regard to the right to vote, and that such a right was connected to "ethnic" origin.
I have not been able to find a mention of ethnic origin in connection with voting rights in the transcript of the Putney debates. Ethnic origin would indeed seem a pressing matter in a Kingdom/Commonwealth inhabited by many Scots and Irishmen.