I went through my copy of "The British Broadside Ballad and its Music", by Claude Simpson, looking for period or very-near-period tunes. My cut-off date was "around 1620". It was a bit fuzzy... if the tune was from 1624, but lots of references to the tune from earlier and few from later, then I'd count it. If it was from 1610 but was invariably associated with songs about the Stuarts, then I might not have put it in this list.
The list below is in alphabetical order, as are the tunes in the book itself.
- All You That Love Good Fellows
- The Black Almain
- Bonny Sweet Robin, or My Robin Is to the Greenwood Gone
- Bugle Bow
- Callino Casturame
- The Carman's Whistle
- Chi Passo
- Come Live With Me and Be My Love
- The Cramp
- Damon and Pythias
- Daphne
- Dargason
- The Downright Squire
- Dulcina
- The Fairest Nymph the Valleys
- Fortune My Foe
- The Frog Galliard
- Go From My Window
- The Gods of Love
- Gray's Inn Masque, or Mad Tom
- Greensleeves
- Heart's Ease
- How Can the Tree
- The Hunt is Up
- I Loathe That I Did Love
- In Crete
- In Peascod Time
- Jig a Jog-Goo
- Jog On, or Eighty-Eight
- John, Come Kiss Me Now
- King Solomon
- Labandala Shot
- Last Christmas 'Twas My Chance
- Light o' Love
- Loath to Depart
- Lord Willoughby
- Lumber Me
- Lusty Gallant
- Monsieur's Almain
- Nutmegs and Ginger
- O Man in Desperation
- Packington's Pound
- Peg a Ramsey, or Peggy Ramsey
- Psalm 81
- Psalm 137
- Quatre Branles
- The Queen's Almain
- Robinson's Almain
- Rogero
- Room, Room for a Rover
- Row Well, Ye Mariners
- Sabina
- Sellenger's Round, or The Beginning of The World
- Shackley Hay, or To All You Ladies Now at Land
- The Shaking of the Sheets
- Shall I Wrestle in Despair
- Sick, Sick
- The Spanish Pavan
- Tom a Bedlam
- Trenchmore
- Walking in a Country Town
- Walsingham
- Watkins's Ale
- Welladay
- What If a Day
- Who Liveth So Merry in All This Land
- Whoop! Do Me No Harm, Good Man
- Wigmore's Galliard
- Willow, Willow
- Wilson's Wild