You can read about Anglo-Catholics here:
en.wikipedia.org/wiki/Anglo_Catholic
They are a party in the Anglican communion that seeks greater identity with the more Catholic elements of their theology over the Protestant influences. Generally, they are a minority party in TAC with foundations most recently rooted in The Oxford movement some 170 years ago.
The problem many Catholics have with the AC claims is one of historical continuity as a “catholic” body. Whereas the East or Old Catholic bodies had a continuity in their catholicity (ie. the recognition of 7 sacraments could generally be seen as continuously intact) the same may not be said of the Anglican Communion.
To many Catholics, this recovery of a more catholic, non-protestant identity may be seen as “too little, too late”. If today a party in the Methodist Church began to use the Roman Missal or the Eastern Divine Liturgy of St. John Chysostom, we would see such external adaptations as being positive, to be sure, but not enough to begin to view that body as a “catholic” body.
Many ACs go through considerable effort and energy to demonstrate that they are possesed of an unbroken lineage of catholicity that was never “Protestant/Reformed”. I am, to date, unconvinced by these claims.
I feel that while they have done an excellent job in creating and promoting a very catholic vision of their faith, it remains problematic to Catholics and Orthodox. Generally we are not comfortable to view them as merely “Catholics in schism” from the rest of the Catholic world in the same way that Eastern Orthodox, Church of the East, Oriental Orthodox, Old Catholics or even Brazillian National Catholics are.