Percy Grainger acknowledged his indebtedness to Lucy Broadwood for his first introduction to English folksong and folksong collecting in a letter to her from White Plains, USA, dated 2 November 1925... "Your work for folksong was always a source of the keenest delight to both my darling mother and myself. I don't know any woman my mother admired more than you....." He first met her at a talk that she gave on folksong collecting to the British Musical Association in March 1905 which fired him up to actively go out and start collecting himself. "Thru the beautiful spirit of that lecture I was led into paths that have meant so much to me and to my life's work, and the popularising of English folksongI have been able to do in US and the European continent etc, all had it's roots in that lecture of yrs, and the fragrance of country melody that it radiated". The lecture sparked off a friendship that was to last until her death in 1929. As already indicated he collected for the first time in 1905, the year of the lecture, and in 1906, Lucy (who was one of the judge's at the Brigg Folksong Competition) and he collected together. Lucy was actually instrumental in her capacity as Secretary of the Folk Song Society in providing him with a phonograph, and he was a pioneer in actually recording rather than annotating songs by hand. He was responsible for making the recordings of Joseph Taylor in 1906 which became the first commercially issued recording of English folksong from a source singer.
Vaughan Williams who was collecting from December 1903 to 1913,(and therefore at the same time as Grainger) was also introduced to folksongs and collecting by Lucy Broadwood (and also according to a letter he wrote to her in 1924 to Bach and Purcell). He was a family friend (living in Leith Hill near Dorking, while her family home was in Rusper on the Surrey/Sussex border nearby), and together with her and two others founded the Leith Hill Music Festival which has just taken place again in Dorking in the last month. Like Grainger he remained a friend of hers until she died. Whether the two composers met at one of the musical soirees and other parties that she held or attended I am unaware - her diaries record the names of various visitors to her home in London, or in Rusper, and both figure frequently therein (as do Holst, Butterworth and other classical music luminaries). It doesn't seem too fanciful to think it might have occurred!
As to Grainger's proclivities and peculiarities, well, they've been quite well documented as other contributors to this thread have indicated. Incidentally he not only collected English songs, but Danish amongst others. (I think his partner of later years may have been Danish - must admit that I'm not a specialist in his area... I'm more interested in Lucy!)
Sorry about the length of this - hope it's of interest.