Sir John Browne, Lord Mayor of London - Didn't marry Alice Swinshed?

From http://www.geni.com/documents/view?doc_id=6000000019248176016

"From the foregoing it will be seen that Sir John Browne's wife was Ann Bel wood, and that there is no indication of his having had a first wife, Alice Swinstead, and by her a son Eobert. He desires prayers to be said for the repose of the soul of his late son Richard; surely he would have done the same for a late wife! The Harleian MS. 1541, folio 135b, has a Browne pedigree, in which Sir John's ancestor is stated to be Sir Anthony Browne, Knight of the Bath to Henry IV. He is given two wives, Alice Swinstead and Ann Belwood, from the former of whom the Brownes of Walcot are made to spring—from the latter the Sir William, Lord Mayor 1507 (instead of 1513, as I have proved). This MS. has long puzzled me. If there is any truth in it, we have at once the Montagu Brownes, of Beechworth Castle, Surrey, established as being of the same stock as those of whom I am writing"

Additional sources in the profile overview

Help with the too many Lord Mayors of same name appreciated