The full version of the quotation from Common Worship on the front page is,
“The service should normally include a psalm or psalms. These might be said or sung in the traditional way, but it is also possible to use a metrical version, a responsive form or a paraphrase such as can be found in many current hymn books. The psalm may occasionally be replaced by a song or canticle the words of which are taken directly from Scripture: a ‘scriptural song’.”
A scriptural song is not a song inspired by scripture. It is a text of scripture like the Benedictus, Magnificat or Nunc Dimittis, which people sing but which comes from elsewhere in the Bible. They are often referred to as Canticles and this is the convention in this collection. There is a tacit convention that some other very ancient hymns come within this parameter. The most well known of these are the Te Deum and Phos Hilaron.
The lectionary provides psalms daily for Morning and Evening Prayer/Services of the Word and for Holy Communion.
Service of the Word:-
From the grammar of the rubrics in Common Worship, it appears that on a Sunday there must be at least one psalm or canticle in a Service of the Word.
Morning and Evening Prayer:-
For full Morning Prayer, the appointed psalmody for the day must be used together with an Old Testament Canticle and the Benedictus. For Evening Prayer it is the appointed psalmody, a New Testament Canticle and the Magnificat. In both cases an additional opening Canticle is optional.
For Compline, the Nunc Dimittis must be used. The other psalms are optional.
It is ambiguous whether the appointed psalm is obligatory in Holy Communion Order One, although it seems generally to be assumed it is not. It is optional in Order Two.
For Daily Prayer, the position is broadly similar, except that there are permitted alternatives to the Benedictus and Magnificat. Whether it is strictly permissible or not, if one is not going to be saying Compline, at Evening Prayer having the Magnificat as the middle canticle and the Nunc Dimittis where the Magnificat is in the book, rather in the style of 1662, works well.
Book of Common Prayer:-
The psalms and canticles are compulsory in 1662 Morning and Evening Prayer. It seems to have been unclear since at least the C17 whether a metrical version may replace the prose version or not.