There are several tunes already available in well-known arrangements. John Duarte's English Suite No.1 has a very nice version of Low Down In The Broom in the middle of 1st movement; the 2nd movement is a theme and variations on The Cuckoo and the 3rd movement has a Robin Hood tune (from Chappell's PMOT) in the middle. His English Suite No.2 (for duo) has versions of The Brisk Young Widow, The Lost Lady Found and Hey Ho Sing Ivy/Gently Johnny My Jingalo.

Benjamin Britten's Folksong Arrangements Vol 6 for High Voice and guitar has arrangements of I Will Give My Love An Apple, Sailor-Boy, Master Kilby, The Soldier And The Sailor, Bonny At Morn and The Shooting of His Dear with accompaniments varying from simple chords or counter-melodies to the startling accompaniment to Bonny At Morn (Jack take note!).

If you widen it to British rather than just English there's other stuff easily available:

Sor's Op.40 Fantaisie sur un air favori ecossais uses Ye Banks And Braes (I think!).

David Russell did an album Message of the Sea with arrangements of Irish and Scottish tunes (the currently published volume has: Bucks of Oranmore, Cherish The Ladies, Niel Gow's Lament for the Death of His Second Wife, Spatter The Dew, Kildare Fancy, Skye Boat Song, Loch Leven Castle, The Bonnie, Bonnie Banks of Loch Lomond, Whiskey You're The Devil, The Fair Haired Boy/Three Little Drummers, The De'il Amang The Tailors).

Scott Tennant from the Los Angeles' Guitar Quartet has published a (fairly straightforward) version of Will Ye Go Lassie Go.

And Gerald Garcia has published some folk-song arrangements too IIRC.

(There are also no end of Carolan arrangements)

Even if you're not interested in these particular arrangements it might give you some ideas for songs/tunes.

Mick