I took her off Sir John Browne, Lord Mayor of London, because I could find no reliable evidence that he had ever married a Mary Amadas.
A bit of searching led me to the information that she had married *a* John Browne, but this one lived in Tavistock, Devonshire. They had one son, Thomas, and he had two sons, of whom the elder was William Browne, Jacobean pastoral poet who was once very popular but now almost completely forgotten.
* https://en.wikipedia.org/wiki/William_Browne_%28poet%29
* http://www.presscom.co.uk/leepriory/leebrowne.html
* https://archive.org/details/poemsofwilliambr01browuoft
I take with the usual sizable amounts of salt the claim that his Browne line can be traced back to Sir Thomas Browne (1402-1460), MP, Chancellor of the Exchequer, etc.