Modern versions of the Nicene Creed use catholic, not Catholic
The original 1662 Book of Common Prayer did use a capitalized "Catholic" in the Nicene Creed.
And I believe one Catholick and Apostolick Church
However, this is more a stylistic choice used at the time in which many important words were capitalized (as the German language still does today). Other words such as "Begotten", "Baptism", and "Sins" are all capitalized. Thus we shouldn't assume that just because it is capitalized that it refers to the Catholic Church.
Common Worship, the 21st century successor to Book of Common Prayer, uses a lower case "catholic" to reflect how the English language and its grammar rules have changed over the last several hundred years.
We believe in one holy catholic and apostolic Church.
The word "catholic" means "according to the whole"
To Be a Christian: An Anglican Catechism, distributed by the Anglican Church of North America, has this to say about the word in its extended catechism:
95. Why is the Church called “catholic?”
The term “catholic” means “according to the whole.” The Church is called “catholic” because it holds the whole faith once for all delivered to the saints, and maintains continuity with the apostolic Church throughout time and space.
Wikipedia reiterates this belief in the following way:
The term ["catholic"] is used also to mean those Christian churches that maintain that their episcopate can be traced unbrokenly back to the apostles and consider themselves part of a catholic (universal) body of believers. Among those who regard themselves as Catholic but not Roman Catholic are Anglicans and Lutherans, who stress that they are both Reformed and Catholic.
In other words, Anglicans have the same quality as both the Roman Catholic Church and the Lutheran Church in that they have continuity with the early Church, but they are also Reformed in that they follow the teachings espoused during the Reformation.