The GAFCON UK website explains the connection here:
…Through affiliation to GAFCON UK, Christians in the British Isles will be connected with this global movement for renewal and mission with its spiritual vitality and evangelistic zeal, doctrinal clarity, wisdom and faithfulness under pressure. As GAFCON is not a new independent church or a rival to the Anglican Communion, membership of GAFCON UK is compatible with being a loyal member of Anglican churches in England, Scotland and Wales while our national churches remain orthodox in their official teachings and policies.
However, those who are concerned about the apparent drift of their denomination can rest secure that whatever happens, there is no need to leave Anglicanism, which is validated not from a human office or place, but from faithfulness to its historic self-understanding. The GAFCON Primates Council stands ready to authenticate those who wish to remain Anglican, but if necessary outside local institutional structures: this has already started with the establishment of the Anglican Mission in England (AMiE)…
The Anglican Mission in England website explains itself thus:
…A variety of Anglican churches are part of AMiE. Some churches are outside the structures of the Church of England. Others remain within the denomination but are experiencing tensions, whilst others have joined to support them…
And there is a list of (currently seven) local churches here.
According to this page:
AMiE is a registered charity (number 1158679) and has an Executive Committee. Andy Lines is the General Secretary of AMiE and Justin Mote is Chair of the Executive Committee.
According to another page on the same site:
AMiE is governed by an Executive Committee consisting of:
Revd Canon Andy Lines (Chairman and Director/Trustee)
Rt Revd John Ellison (Chair of Panel of Bishops)
Revd Canon Tim Davies
Revd Lee McMunn (Mission Director)
Mr. Brian O’Donoghue (Secretary and Director/Trustee)
Revd Jonathan Pryke
All the members of the Executive are required to hold a ‘complementarian (Equal and Different)’ position on women’s ministry, but AMiE will support all churches who hold to the Jerusalem Statement and Declaration.
GAFCON UK says:
GAFCON UK is led by a Task Group, whose members are:
GAFCON UK is overseen by an advisory Panel of Reference: