I used to keep a watching brief of Independent Catholics; at one point I even thought I might become one. I had correspondence with one of these groups until they messed about with a friend and when they objected to a blog entry in which I said they were positive about homosexuality and me stating that there is a positive connection between such groups and homosexuality, in contrast with many Churches.
From time to time I have got into further trouble making lists of where some of these sometimes called Episcope Vagantes can be found. This is because they keep moving and then get stroppy when the list falls out of date and they find themselves still associated with a group with which they have fallen out. I do change the list when asked. Once an email kept landing in my junk mail and then I was threatened with a lawyer simply because of a listing that was now out of date.
A grouping I looked at closely was the Liberal Catholic Apostolic Church, set up after numerous groups and name changes and steered by the talented musician Bishop John Kersey. He wrote lots of webpages for this new grouping, and he headed it with Bishop Andrew Linley and the new boy Bishop Alistair Bate, one time lay leader of Glasgow Unitarians (I have discovered his picture on a copy of The Inquirer). Now, incredibly, Kersey and Linley have gone and they are not even listed in the The Independent Liberal Catholic Fellowship. Linley joined Kersey in a new set up, The Apostolic Church of the Divine Mysteries, although it has a direct connection with Kersey's somewhat spiritual mentor Bishop Bertil Persson (who also wrote about those Bahais who accepted the Guardianship of Mason Remey). His new outfit claims to be more traditional Catholic than traditional, in that it is pre-Nicene in its observances. I don't see the commitment once held towards the Liberal Catholicism of Leadbeater and Wedgwood, though this may be there, nor can I see what has happened to any religious connections with the private and independent and immensely named European-American University that has ad hoc courses and publications linked to these concerns.
Now the news is that LCAC has decided to drop having a Metropolitan, and have decided on a more collegiate Presiding Bishop approach, with Alistair Bate as the first. Good luck to them. I always thought he had a better strategy in developing, in effect, a congregation based around esoteric Christianity up there in Edinburgh; you cannot have a Church simply based on ordaining people from each and every tradition and making bishops as you go along, even if there are people receiving rites of passage in the meantime. Whether a congregation is online or regional or local, you have to have a gathering. Otherwise it is too fantastical and like playing at it. I understand he still takes services at Newcastle Unitarians as well as doing some Druid type workings.
I think the argument can be made that they draw from the Free Catholics of Rev. Joseph Morgan Lloyd Thomas (Unitarian: 1868-1955) and W. E. Orchard (Congregationalist), and they might mention Ulric Von Herford, the Unitarian minister who became an animal rights bicycling and monastic church ministering Liberal Catholic Bishop, but it's a bit much to claim Francis David of Transylvania, who became entirely Protestant and of the left wing of the Reformation. When Knut Heidelberg was ordained minister in Hungary and took this back to Norway, it was specifically stated in the ceremony that they did not believe in apostolic succession in the sense that Catholics do. It was a procedure of recognition, not handing down some sacred deposit.Of all of them the most ecumenical and mainstream is probably the Open Episcopal Church associated with the Most Reverend Jonathan Blake, a self-financing bishop with a high media profile. His outfit looks to the Old Catholic prior to the Liberal Catholic development and, like all these groups, is socially inclusive if 'regular' in a doctrinal sense. My interest is inevitably more in the liberal groups, even the stranger ones: I'm just not into magic.