Introduction: The Gospel Standard is a Strict Baptist magazine first published in 1835 by William Gadsby. Churches which align themselves with the magazine are known as "Gospel Standard Baptists" or "Gospel Standard Strict Baptists". https://www.gospelstandard.org.uk/Magazines/Overview
Here is an extract from an article about the ‘English Strict Baptists’ which discusses the desire of The National Strict Baptist Federation (formed in 1946) to achieve unity. The article concedes that the Federation has not brought the desired unity, even though efforts were renewed between 1962 and 1965 to obtain such unity. The following conclusion is reached on page 35:
If these Churches are to give the world a valid reason for their separate existence outside the Baptist Union, and to halt the decline of congregations and closure of chapels, something very drastic needs to happen. The prayer of those of all generations who are genuinely concerned about this sad state of affairs is that there will be a wholesome return to the doctrines which were held dear by the Particular Baptists who formulated the 1677 and 1689 Confessions of Faith. It is believed that by a return to such doctrine there will come reform, renewal and unity amongst the Churches. Source: https://www.biblicalstudies.org.uk/pdf/bq/21-1_030.pdf
So far, the drastic does not appear to have happened.
A different source of information https://www.the-highway.com/Sonship_Preface.html comes from a book written in 1860 by J. C. Philpot of the Baptist movement entitled 'The True, Proper and Eternal Sonship of the Lord Jesus Christ':
Today, some appear to be Exclusive Brethren and are headed by an Australian man, (and administered from Australia) calling themselves 'Plymouth Brethren' but their teaching contradicts the Leader of that, original, movement (J N Darby) who is quoted as saying: “If I hold the Son only as son from incarnation - I lose everything.”
From what I have discovered, the Brethren movement split in 1890. One section led by F. E. Raven (the cause of the split) was succeeded by James Taylor Senior, who held at least some of Raven's views. Raven and Taylor taught that the expression 'son of God' refers only to the One who came in flesh after his incarnation and not before. Those who disagreed with this view, holding to the ‘eternal son-ship of Jesus Christ’, departed.
Conclusion: I have not found any evidence to suggest that the Strict Baptists and the early Plymouth Brethren attempted to reconcile their differences in order to achieve unity. Of course, that does not mean no attempt was made. However, the sad fact is that both groups have gone their separate ways, resulting in isolationism.