The Litany is a traditional devotion during Lent. There are two options presented to us in the Anglican Breviary to say the Litany:
1) one can say the Litany immediately following the Seven Penitential Psalms as given in the Breviary,
2) one can say the Litany immediately following the Seven Penitential Psalms as given in the Book of Common Prayer with very few additions to restore the Prayer Book Litany from radical Protestant mutilations (Abp. Cranmer’s first reformed Litany included the suggested additions to the current Prayer Book Litany).
For those of you who possess the Lancelot Andrewes edition of the Book of Common Prayer the Litany can be used as is given therein. This edition of the BCP reflects the way Orthodox Christians may adapt the Book of Common Prayer for their use and does not in every respect reflect an Anglican use.
Whichever version of the Litany one opts to use when it is ended one can simply conclude the Office or continue saying the Divine Office with Prime and the Martyrology.