The London Baptist Confession of 1689 says in its second chapter:
“The Lord our God is but one only living and true God; whose subsistence is in and of himself, infinite in being and perfection…
In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided: the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son; all infinite, without beginning, therefore but one God, who is not to be divided in nature and being, but distinguished by several peculiar relative properties and personal relations; which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on him.”
Here we see them begin their treatment of the Trinity by saying that the one God is a person “whose subsistence is in and of himself”. Subsistence is a philosophical term for person, when it refers to something of a rational nature, such as God, or an angel, or a man. What is more clear in identifying him as a single person is their explicit use of singular personal pronouns.
Had they stopped there and called this person who is the one God the Father of our Lord, there would have been no disagreement either with scripture or with the faith of the ancients. But we see further in the chapter that they expressly identify this person of the one God as being “three subsistences, the Father, the Word or Son, and Holy Spirit”. So they have explicitly declared the one God to be a single subsistence who is three subsistences, or put into common language, one person who is three persons.
If anyone doubts that this was the intention of those who framed the confession let them notice that later in the same paragraph quoted above they again use a singular personal pronoun in regard to all three together taken as one God, making again explicit their erroneous belief in that the one God is one person who is three, instead of being identical with the Father of our Lord as the scriptures teach (see: We Believe in One God, the Father Almighty).
And so this baptist plagiarism of the Westminster Confession of Faith is shown to be expressly semi-modalistic. The Westminster Confession maintains a better statement on these matters, being ambiguous enough to be taken either orthodoxly or otherwise, unlike the baptist modification that specifies an anti-trinitarian belief explicitly.
Until this articulation of the doctrine of the Trinity is recognized as being problematic, there is little hope of seeing reform in this area among those who subscribe to this confession.