Maynard was the son of John Maynard, who had been MP for St Albans in the first Parliament of Mary I of England in 1553-1554 (being one of the 39 members who absented themselves, rather than acknowledge the authority of the Pope), and his second wife, Dorothy, daughter of Robert Perrot.
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Sir John Maynard, another son of Sir Henry Maynard, represented Essex in the Long Parliament but was impeached for high treason, expelled from the House of Commons and imprisoned in the Tower of London.