I'm not familiar with that customary, but full music for the Church of England's official versions of compline (also heard in other Anglican churches and college chapels) is available here:
This site also provides a translation of compline according to the Use of Sarum (still theoretically allowed under Quo primum), which is really fabulous:
To participate in the discussions on Catholic church music, sign in or register as a forum member, The forum is a project of the Church Music Association of America.