Here's a random selection of some of my favourite source material for traditional melodies from the British Isles:
A Northern Lass - Traditional Dance Music of North-West England - compiled by Jamie Knowles, published by Dave Mallinson Music (1995). Suitable for any melody instrument.
The Complete Country Dance Tunes from Playford's Dancing Master - edited by Jeremy Barlow, published by Faber Music. Playfords English Dancing Master has been around for hundreds of years and has been updated several times (my version was published in 1985).
The Complete Works of O'Carolan, Irish Harper & Composer - Ossian Publications (1984). One of the first, if not the first, complete compendiums of O'Carolan's surviving music. Suitable for any melody instrument.
O'Neill's 1001 Jigs, Reels, Hornpipes, Airs and Marches - The Irish Music Collection, Waltons Manufacturing Ltd, Dublin (1986). Suitable for any melody instrument.
One Thousand English Country Dance Tunes - published by Michael Raven, distributed by Music Exchange Manchester (1983). Suitable for any melody instrument.
I have other sources for Scotland and the Isle of Man etc, including on-line resources. Some of the tunes I've arranged have come from memory - from sessions (where I've learned by ear) or from childhood hymns (medieval music and folk tunes were a staple of the Victorian church - lyricists would take the tune and add new words, which has been terrific for ensuring the survival of many melodies).
Attribution: the music of the British Isles has travelled around the Islands in various incarnations, meaning the origins of many tunes are disputed or just plain forgotten. Hundreds of traditional melodies have different versions of the same original, now rooted in different regions/countries. I've found that websites like The Session are terrific for the tunes themselves, but are variable in terms of reliable attribution. The heritage of what's often termed Celtic music isn't (as is sometimes assumed) simply Irish and Scottish, it grew from the British Isles as a whole, and so includes English and Welsh music along with that of smaller Islands such as the Isle of Man. We often share tunes.
Here's a link to The Session website, where you can find and learn traditional tunes, use playback at various speeds to practise alongside, and print out the dots. The site is advertised as Irish music, but it contains traditional folk tunes from all over the British Isles and beyond:
When I'm working out guitar accompaniments, I use the playback feature on The Session to practise to.