Invocation of Saints is not found in any authorised Church of England liturgies (BCP1662/Common Worship 2000). Most of the Collects for Sundays that we find in the Book of Common Prayer have come down from old Sacramentaries such as the Leonine, Gelasian and Gregorian Sacramentaries which date from the 5th/6th centuries. The English Reformers retained most of these these Collects, translating them from Latin to English. However, most of the Collects for Saints Days found in the BCP were mid 16th century compositions as the old Collects usually contained some reference to the merits or intercession of the Saints.
The practice of the Invocation of the Saints in the Church of England dates to the Ritualist movement of the latter half of the 19th century. A wide range of liturgical practices many now taken for granted were then highly controversial. Clergy were prosecuted under the Public Worship Regulation Act of 1874. (Practices such as the use of Eucharistic vestments, elevation of the host, use of incense, lighted candles on the Altar (especially the 'Big Six'), using unleavened wafer bread, veneration of the BVM, invocation of Saints...the list could go on).
During the Medieval period, the invocation of Saints led to much superstition. In England there were cases where even statues of Saints were credited with miraculous or supernatural powers. The English Reformers erred on the side of caution with regard to the invocation of Saints - they felt there was no scriptural warrant for the practice and that we can't be certain that the Saints in heaven have the ability to hear our prayers - this would give them God-like attributes.
Having said that, you may find practices such as the invocation of Saints in Anglican churches of more advanced Anglo-Catholic persuasion. I once attended a Forward in Faith church in the village where I then worked where at appropriate times of the year we sang the Litany of Saints. My Cathedral Church will often end the Intercessions on Marian feast days with the Hail Mary.
Thank you.
