I’ve searched high and low to find an answer to this question, but the best I could come up with was this statement from the Baptist Union of Great Britain:
Many Baptists will want to welcome and affirm those who have a different story to tell of how they have been baptised and come to faith, while still declaring our conviction that believer’s baptism is the pattern that is set out for us in scripture: https://www.baptist.org.uk/Groups/220594/Believers_Baptism.aspx
The Baptist Union has no problem in welcoming and affirming a Christian who wasn’t baptised in the manner proscribed by the Baptist church, but says nothing specific regarding the situation where an adult Christian was baptised by full water immersion within another denomination.
One U.K. Baptist church said this: “Because Baptists do not accept infant Baptism or christening as true baptism, then there is normally no objection to the baptism of a believer who has been christened as an infant.” Again, this does not address the specific situation you ask about.
When I became a Christian 23 years ago I understood that I could not become a full member of the Baptist church unless I studied, understood and accepted their core tenants of belief and, as an adult, confessed Christ Jesus as my Lord and Saviour. I had been baptised (full water immersion) as a 13 year old but I did not consider that baptism to be valid. The minister had no problem with my request to be re-baptised. Neither did he ever say he thought my original baptism was invalid. He just waited for me to make up my own mind and after he was assured that I knew what I was doing, I made a public confession of my faith and was baptised by full water immersion.
In all the years of my association with the Baptist church I have never read any statement about the validity (or otherwise) of full immersion baptism of an adult performed by another denomination. Of course, each Baptist church is an independent entity and each local Baptist church appoints its own ministers. https://www.baptist.org.uk/Groups/220484/Who_are_Baptists.aspx
The question of full membership within the Baptist church may be dependent upon having submitted to believers’ baptism as performed by the Baptist church. But nobody has to be a member of a church in order to be saved. Becoming a member simply means you get to participate in the election of ministers/deacons and to vote when changes are put forward. The importance of believer’s baptism within the Declaration of Principle of the Baptist Union of Great Britain may shed some light on your question:
The Basis of the Baptist Union is:
That our Lord and Saviour Jesus Christ, God manifest in the flesh, is the sole and absolute authority in all matters pertaining to faith and practice, as revealed in the Holy Scriptures, and that each Church has liberty, under the guidance of the Holy Spirit, to interpret and administer His laws.
That Christian Baptism is the immersion in water into the Name of the Father, the Son, and the Holy Spirit, of those who have professed repentance towards God and faith in our Lord Jesus Christ who 'died for our sins according to the Scriptures; was buried, and rose again the third day'.
That it is the duty of every disciple to bear personal witness to the Gospel of Jesus Christ, and to take part in the evangelisation of the world. https://www.baptist.org.uk/Groups/220595/Declaration_of_Principle.aspx
Given the flexibility and independence within U.K. Baptist churches, I suspect that the Baptist Union does not take a hard and fast stand about the validity of full water baptisms performed by other denominations on consenting adults. No doubt the subject is covered in theological college, but I’ve never seen anything in literature that can be accessed by laypersons.
The minister in the Baptist church I attended even performed a baptism by sprinkling water on the head of a very old lady who had been coming to the church for decades, and finally got round to confessing that she had been putting it off for too long. Full water immersion would not have been an option, so any “rules” about baptism were waived. Let’s face it, the point of salvation is to confess Christ Jesus as your Lord and Saviour and although Baptists have a firm view on how baptism should be done, they also reject the notion that salvation depends on that.