The Anglican bishop Cirlot wrote a book on whether or not apostolic succesion is true (incidentally, its title is Apostolic Succession: Is It True? Practical name for his book, eh?). One of the objections he had to deal with to the Catholic position was that there seems to be a lot of Christians outside of of the visible Church. The Catholic view (not Roman–just universally held by Christians across the centuries; this is the view shared by Anglicans, Orthodox, and Roman Catholics) is that the Church is an organization with visible criteria of membership, instituted directly by Christ with a heirarchical structure that has sacramental grace. The Church is a polis, a city or nation of sorts–not an earthly one, surely, but a true polis none the less.
Cirlot mentions the arguments of the archbishop of Cantebury William Temple for the conclusion that Protestants are fully the Church in just as unqualified a way as the Catholics (which here designates Anglicans, Orthodox, and Romans). The main argument is from the superabundance of grace that we see outside the Church. The moral and spiritual character of Protestants is not excellent across the board; there are some bad apples. But there are so many good Protestants that it makes the Catholic view of the Church improbable. How could a Catholic possibly deny that a good Protestant is in the Church?