From Wikipedia: The opening music and "Corn Rigs" are arrangements of the Robert Burns ballads "The Highland Widow's Lament" and "Rigs O' Barley", respectively. The instrumental parts of the score are based on traditional Scottish, Irish, and English tunes such as "Miri it is", the strathspey "Robertson's Rant" jig, and "Drowsy Maggie" reel. "Chop Chop" is based on the nursery rhyme "Oranges and Lemons". "Procession" is an arrangement of the tune of the Child Ballad "Fause Foodrage". Although some of the music is Scottish, and the film is set in the Hebrides, no traditional Scottish Gaelic numbers are featured.
Giovanni “had 6 weeks to research, prepare, compose and record the soundtrack, all of which had to be done before the first day’s shooting.” - Cinefantastique, Vol 6, #3 (1977) He had written 8 or 9 songs but some had to be cut as Shaffer felt it slowed the plot down to be having music "every 20 seconds." (Brown)
The only London Symphony Orchestra involvement was "Maurice Murphy playing the very long ramshorn note outside the cave (but on a trumpet of course) -
and the closing credits." Gary Carpenter, 12/2/15, Facebook Wicker Man group. Gary amends this on 9/23/17. See end credits music page. (“Just a bit of lost information about musicians. The three trumpet players at the end of the film were not LSO but Colin Clague, Cliff Haines (an older session player who lived in studios most of his career) and Stephen Hetherington. I'm grateful to Colin (who plays the closing high note) for this!” and "On screen brass/wind band musicians didn't play on the sessions - they were army players. Trumpets on that (recording) session were Colin Clague and John Hammond.")
From Gary's website: recordings were done at DeLane Lea Wembley, Pye and Shepperton, excluding the on-set recordings of The Tinker of Rye and The Landlord's Daughter's vocals.
Here are some pictures, courtesy of Lesley Mackie, of the recording process.
See also audio recordings
Some background on the recording process here. ("Band on the wall” interview, Soundcloud)
Some notes from that:
Paul wanted to engage Pentangle and (Comus?). He didn’t try that hard… Procession has a resemblance to Pentangle track, another to Benjamin Britten. Eye on boat is Egyptian. Only one piece is Scottish, (use the Irish version of Drowsy Maggie). Fife used in fire leap. Gary went over to Cecil Sharp House for a harp… Mike Cole concertina, Ian, Andy, Peter Brewis good on everything, Hardy didn’t want any electrical instruments, Paul snuck them in to spite him for the cave sequence. DeLane Lea used 16 track, one of the first to have a 24 track. Pye was only 8 track. Louis Austin (Westside?) did post mix. Incidental music recorded at Shepperton. Recorded to two track there. Bass gtr covered with parachute tarp. Procession and summer is a comin in were recorded in two different places. Never read David Pinner book. He just got a script which he has since lost. (Can’t understand what they are talking about.. remake…) Saw it with WM fans you could tell from the length of their beards. Another set of prints in New Orleans… as Deeley trashed it. Music doesn’t date apart from the rock and roll. Voices close mic’d all the time. Paul liked the sound of the hand going up and down the strings. Stereo release of most of the important songs. He carried it around with him. He couldn’t use it cuz he didn’t have the rights. He played cassettes, didn’t want to use 7 & 1/2 ips masters. Talks about Jonny Trunk. John Craig of First Night Records connected with British Lion. He likes the Silva Screen relationship. He still has 7&1/2 ips master. Paul did post production at Louis Austin’s place. Wanted to re-record Willow song with Lesley Mackie. Everything else was the same. Tinker of Rye was recorded on site so had to re-do it. Explains how Tinker of Rye worked. Voices are the voices you hear in the film. The accompaniment is not. Landlord’s Daughter was re-recorded as film version was done “wild” and not edited properly. Talks about Michael Nyman work. …
Music in each version
Individual songs and other music used in the film
Dream sequence (cut from all versions)
The best review of the music I've seen here.
Songbook available here.
See these two BFI videos: Gothic - Sing Cuckoo, The Story of the Wicker Man soundtrack, and Folk Musicians discuss the Wicker Man.