Legal letters from the campaigners have been delivered to the Human Research Authority (HRA) and the Medicines and Healthcare products Regulatory Authority (MHRA), which have given the puberty blockers trial ethical approval.
Mr Streeting, along with NHS England, King's College London and the South West London and Maudsley NHS Trust have also been notified.
A Department of Health and Social Care spokesperson said medical care "must always be based on solid evidence, and children's safety must come first".
They added: "This trial will help provide the evidence that is currently lacking. Its approval came only after extremely rigorous safety checks and with multiple safeguards in place to protect young people's wellbeing - including clinical and parental approval."
In a statement, the MHRA said the safety of participants was "always" its priority and its role was to "rigorously assess" clinical trial submissions to ensure they met "the appropriate regulatory standards of participant safety and scientific integrity".
It said it also continually reviews the approval of the trial as it proceeds.
A spokesperson for the Health Research Authority, said the Pathways trial had "all the necessary regulatory approvals that it needs to begin".
It explained that a Research Ethics Committee, made up of people including healthcare professionals and members of the public, look at research proposals and give opinions about whether they are ethical.
The KCL research team said: "Clinical care should always be underpinned by robust evidence, and this study will help provide a better understanding of how to treat and care for young people with gender incongruence."
The researchers said children taking part in the study would need the consent of their parent or legal guardian, plus the agreement of their lead clinician and a multidisciplinary team.
A spokesperson for charity Stonewall said it was "vitally important" that all LGBTQ+ people, including young people, have access to high-quality, evidence-based and timely healthcare.