The RCIA introductions for England and Wales, are at
liturgyoffice.org.uk/Resources/Rites/RiteRitual.html . (The USA edition has different paragraph numbers.) Section 5 is the most relevant to you, “RECEPTION OF BAPTISED CHRISTIANS INTO THE FULL COMMUNION OF THE CATHOLIC CHURCH”. It has:
“391 The baptised Christian is to receive both doctrinal and spiritual preparation, adapted to individual pastoral requirements, for reception into the full communion of the Catholic Church.The candidate should learn to deepen an inner adherence to the Church, where he or she will find the fulness of his or her baptism. During the period of preparation the candidate may share in worship in conformity witli the provisions of the Ecumenical Directory.
Anything that would equate candidates for reception with those who are catechumens is
to be absolutely avoided.”
Despite this, note that the RCIA book also includes:
“Appendix 1
CELEBRATION AT THE EASTER VIGIL OF THE SACRAMENTS OF INITIATION AND OF THE RITE OF RECEPTION INTO THE FULL COMMUNION OF THE CATHOLIC CHURCH
418 Pastoral considerations may suggest that along with the celebration of the sacrament; of Christian initiation the Easter Vigil should include the rite of reception of already baptised Christians into the full communion of the Catholic Church. But such a decision must be guided by the theological and pastoral directives proper to each rite.The model provided here simply arranges the ritual elements belonging to such a combined celebration. But the model can only be used properly in the light of nos. 198-210, regarding celebration of the sacraments of Christian initiation, and of nos. 387-399, regarding the rite of reception into the full commuion of the Catholic Church.”
Paragraphs 419-421 give more information on this.