Short answers, pulled from the story.
Antonio Fernandez Carvajal led a considerable number of Sephardic merchants who settled in London during the mid-17th century. These individuals formed a secret congregation despite strict legal restrictions on Jewish presence.
The Bevis Marks Synagogue opened its doors in 1701 following earlier activities at Creechurch Lane. These locations stood as the first Jewish religious places since the Edict of Expulsion of 1290.
Antonio Fernandez Carvajal and his associates held prayer meetings at Creechurch Lane while outwardly passing as Spaniards and Catholics. This location hosted gatherings that became known to the government as Jewish faith gatherings.
England remained the only country excluding Jews until theological arguments advocating return gained traction through works like Menasseh Ben Israel's Hope of Israel published in 1650. Public opinion prepared for sympathetic treatment through the Puritan movement before any official readmission occurred.
Antonio Fernandez Carvajal and his merchant network enabled them to provide intelligence to Oliver Cromwell's government regarding plans by Charles Stuart in Holland. John Thurloe served as Cromwell's secretary and received important information from this group about actions by Spaniards in the New World.