It is sometimes described as High Church.
Anglo-Catholicism was promoted from the 1830s onwards by a group known as the Oxford Movement or Tractarians, whose leaders included John Keble, John Henry Newman and Edward Bouverie Pusey; Newman eventually converted to Catholicism.
Traditionally, Anglo-Catholicism has been seen as attractive to, and sympathetic to, gay priests.
Readers of Brideshead Revisited may recall Cousin Jasper's warning to Charles Ryder:
Beware of the Anglo-Catholics - they're all sodomites with unpleasant accents.