Books, Articles, and Academic Studies - Music
There are a small number of studies of vernacular instrumental music. These include books, articles, and academic theses, which I will add as I become aware of them.
See also Dance Bibliography for research on Dance.
Bartram, Chris; The Fiddle in Southern England ; Yorkshire Dales Workshops, n.d.
Bearman, C.J.; The English Folk Music Movement 1898-1914 part of Doctoral Thesis. PDF
Boyes, Georgina (2010). The Imagined Village: Culture, ideology and the English Folk Revival. London: No Masters Cooperative Limited. ISBN 978-0-9566227-0-9
Campbell, Stephen William John; Doctor of Philosophy University of York,Department of Music, October 2012 Reconsidering and Contextualising the Vernacular Tradition: Popular Music and British Manuscript Compilations (1650–2000) PDF
Chandler, Keith; Articles on English traditional musicians on the Mustrad website 
Chappell, William; Popular Music of the Olden Time. 1855. 2 Vols. A collection of Ancient Songs, Ballads, and Dance Tunes, illustrative of the National Music of England. With short introductions to the different reigns and notices of the airs from writers of the 16th and 17th centuries. Also a short account of the Minstrels. By W. Chappell, F.S.A. The Whole of the Airs harmonized by G.A. MacFarren. Never out of print! PDF at IMSLP
Cooke, Peter; The Fiddle Tradition of the Shetland Isles; The author's PhD thesis completed at the University of Edinburgh in 1982. The book has long been out of print. Zip file with 34 accompanying tracks. School of Scottish Studies
Cooper, Paul; A series of papers on the subject of dances of the Regency Period 
Dellow, Becky; Fiddler's Tunebooks; PhD student and fiddle player, Rebecca Dellow, writes about her musicological research into C19th amateur musicians and their manuscripts. 
Eldon, Jim; Article on Billy Harrison, fiddler, on the Mustrad website 
Emmerson, George S.;Rantin’ Pipe and Tremblin’String: A History of Scottish Dance Music; Montreal:McGill – Queen’s University Press, 1971.
Faulds, Katrina; Invitation to the Dance:Social Dance and Dance Music in the English Country House 1800-1850; PhD Diss, University of Southampton; follow link to PDF
Faulds, Katrina (2015); Invitation pour la danse: Social dance, dance music and feminine identity in the English country house c.1770-1860; University of Southampton, Faculty of Humanities, Doctoral Thesis , 389pp Link
Fleischmann, Aloys and Mícheál ÓSúilleabháin; Sources of Irish Traditional Music C. 1600–1855; New York and London:Galland,1998.
Gammie, Ian and Derek McCulloch; Jane Austens Music: The musical world of Jane Austen; St Albans: Corda Music Publications, 1996.
Gammon, Vic; Manuscript Sources of Traditional Dance Music in Southern England, PhD thesis, published in Traditional Dance 4 (1986): pp53-72. Available, with much else, on Vic's personal web site ;
Gammon, Vic; Articles on English traditional musicians on the Mustrad website 
Hall, Reg; I Never Played to Many Posh Dances; Major work on English Dance music, available as PDF download from Mustrad website 
Hall, Reg; A Few Tunes Of Good Music: A History of Irish Music and Dance in London; Major work (1000 pages) on Irish Dance Music, available as a flip book
Harker, Dave; FAKESONG: The Manufacture of British Folk Song, 1700 to the Present Day (Popular Music in Britain) 1985
Heath-Coleman, Philip; Articles on English traditional dance music on the Mustrad website 
Hield, Fay; Research in Folk Music. webpage
Holderness, Chris; Articles on English traditional musicians on the Mustrad website 
Howson, John; Articles on English traditional musicians on the Mustrad website 
Johnson, David; Music and Society in Lowland Scotland in the Eighteenth Century; Edinburgh: Mercat Press, 2003
Keegan-Phipps, Simon; Teaching folk : the educational institutionalization of folk music in contemporary England; 2008; PhD Thesis, Newcastle University; Link
Kuntz, Andrew; Tune History Articles, An extensive series of individual tune histories written as articles for Fiddler Magazine over a long period by A. Kuntz. PDFs
Little, Alice; Research, PhD on the work Of John Malchair 
Long, Paul; An Entirely New Englishness. The Post-War Folk Revival and the Renegotiation of National Identity. 2007 Ch.6
Long, Paul; The Fantasy of the Lower Classes: The Post-War Folk Revivaland the Politics of Culture 2008 Ch.2
Marsh, Christopher; Music and Society in Early Modern England, review
Murphy, Judith; SELLING COALS TO NEWCASTLE:The media and publishing in relation to North Eastern folk music, 1945-1975 PDF
Pendlebury, Celia; (2015) Jigs, Reels and Hornpipes: A History of "Traditional" Dance Tunes of Britain and Ireland;  MPhil thesis, University of Sheffield. (on the page, go to the box labelled "text" to access). Also contains a useful bibliography.
Plus a thoughtful review of the above 
Pickering, Michael; Articles on English traditional musicians on the Mustrad website 
Seattle, Matt; Harmonic Proportion; Extracted from The Master Piper (3rd edition), Matt Seattle, Hawick, 2011, with permission; "The term Harmonic Proportion, already used in art and architecture, is applied here to a group of ideas or principles which have gradually coalesced from a study of Border pipe tunes"
Stevens, Greg; Article on William Irwin on the Mustrad website 
Summers, Keith; English Country Music: A Tradition in Isolation?; Article on the Mustrad website 
Williams, Dave; Stan Seaman, Melodeon Player; Article on the Mustrad website 
Yates, Cynzia; Excavating Notes: Archaeology of Canon in Manx Traditional Music, PhD Ethnomusicology, Cardiff University 2013, website
Yates, Cynzia; "…while the others did some capers": the Manx Traditional Dance revival 1929 to 1960, Master of Arts in Manx Studies Final dissertation, University of Liverpool 2006
Yates, Cynzia; The Andreas Flute Book, Batchelor of Music Final year dissertation, University of Wales, Cardiff 2002
Yates, Mike; Articles on English traditional musicians on the Mustrad website 
International Council for Traditional Music:Study Group on Historical Sources of Folk Music. Conference Report, Copenhagen April 1995. Facsimile available at Google Books. You may need to translate some of it!
National Early Music Association, The Hornpipe (© 1993) Papers from a Conference held at Sutton House, Homerton, London E9 6JQ 
Play It Like It Is : Fiddle and Dance Studies from around the North Atlantic. Russell , I & Alburger , M A (eds) 2006 , Play It Like It Is : Fiddle and Dance Studies from around the North Atlantic . Elphinstone Institute Occasional Publication , no. 5 , University of Aberdeen, Elphinstone Institute , Aberdeen . PDF
The Folk Music Journal. The peer-reviewed journal of the EFDSS. Contents pages are on the FMJ website.
Magazines containing published un-refereed learned articles
English Dance & Song is the organ of the EFDSS. It has a web site where extra content is included for each issue.
Musical Traditions (Mustrad) Internet magazine containing many articles and reviews. 
See also Dance Bibliography for research on Dance.