My info on the title of Cox's play is from Charles Read Baskervill, The Elizabethan Jig and Related Song Drama (1929; Dover, 1965, p. 123) ["Nymph Oeone" should have been "Nymph Oenone"], which contains the full text of "Singing Simpkin" (pp. 444-49) where the Maypole song is not. "Staines Morris" is in The [English] Dancing Master (1651-1663 editions; "English" was dropped from the 2nd and later editions). Although the title given is "Stanes Morris", it is spelled "Staines Morris" on the contents page.

The following are the notes to the tune by Margaret Dean-Smith in Playford's English Dancing Master 1651 (Schott & Co., 1957, p. 73 [p. 87 in Playford's original]).

STA[I]NES MORRIS
1. Ballet's Lute-Book, c. 1600.
2. Robert Cox, Actæon and Diana, 1656, 'Come ye young men.'
3. CNA [Chappell, National English Airs] 171, CPM [Popular Music of the Olden Time] 125-6, gives the above information, which is repeated by WELLS ['Playford Tunes and Broadside Ballads'], who, quoting Frank Kidson, confirms that the tune of 'Come ye young men' (The Maypole Song) can be identified with 'Staines Morris.' What Professor Wells says about the country dance being 'set to an older morris tune associated with the locality of Staines on the Thames' is, however, most questionable. 'Staines' may be a personal name--cf. 'Mr. Staines Delight' in Farmer's Consort, 1686, secondly, there is no evidence that the morris dance, always highly localized, existed at Staines, and records of it in the counties of Middlesex, Surrey or Berkshire, which meet at Staines, are very slight. The tune is none-the-less very apt to the morris: the Playford version is modal in a much higher degree than 'Come ye young men,' the form in which it is best known. In a context similar to Actæon and Diana it was incorporated into Sir George McFarren's May-Day Cantata 200 years later. These examples of the tune provided a particular exhibit in the Musicians' Company Exhibition of 1904: 'Is it not a striking illustration of the extraordinary interest of the Exhibition,' said Sir Edward Clark, lecturing, 'that you can see, if you are interested in the 'Staines Morris' tune, the original Lute-Book of William Ballet, the very rare first edition of Playford's Dancing Master and the original Ms. score of MacFarren's May Day?' As an illustration to Sir Edward Clark's discourse Miss Adela Vern 'here played on the pianoforte the 'Staines Morris' tune with its imitations of the tabor and the pipe.'
4. The tune 'Anima Christi', No. 327 in The Methodist Hymnbook has been identified by Miss Gilchrist as the 'Staines Morris' tune: it yet remains to identify either form with the 13th century melody 'Anima Christi' known nowadays as a plainsong motet.
The dance is a kissing-dance of processional type sufficiently appropriate to May-day, but in no way a 'morris.' It survives in Wright's Country Dances, Vol. I, c. 1720.

~Masato