Except the Evangelical Presbyterian Church in England and Wales and the Free Presbyterian Church of Ulster, both of which have a few congregations in England, I am not aware of any other Presbyterian churches in England. I know that the Presbyterian Church of England merged to form the United Reformed Church some years ago, but surely there must be some that did not merge?
I'll describe the denominations you mention, for the purpose of completeness, but you've only left out one small denomination, from what I have found. The denominations are:
- United Reformed Church (founded 1972)
- Formed by the merger of the Presbyterian Church of England and the Congregational Church in England and Wales.
- Theologically liberal, and no longer exclusively presbyterian.
- Free Presbyterian Church of Ulster (1951)
- Theologically conservative (Westminster Standards, but permitting credobaptism). Based in Ireland; only a small minority of its churches are in England.
- International Presbyterian Church (1969)
- Theologically conservative (Westminster Standards and Three Forms of Unity). One of its four presbyteries is in the UK, of which several churches are in England
- Evangelical Presbyterian Church in England and Wales (1987)
- Theologically conservative (Westminster Standards). About 20 congregations, most of which are in England.
The biggest Presbyterian denomination in England is the United Reformed Church (it also has congregationalists).