According to Schulz and deVienne (Nelson Barbour: The Millennium's Forgotten Prophet), there was interest in the UK from the 1860s. They name and connect to articles by an Eliash H. Tucket, a Baptist turned follower of Barbour. A Christadelphian journal reviewed Barbour's Midnight Cry booklet and there were Herald of the Morning subscribers in the UK. On their web sites (one of which is invitation only) they reprint the review.
A Canadian writer noticed Zion's Watch Tower in an article published in Rainbow. Earlier Rainbow had reviwed Three Worlds. The first concerted effort in the UK was by two Americans sent by Russell, John Corbin Sunderlin (a pioneer era photographer and former Methodist minister) and Joseph J. Bender. The contracted the printing of thousands of copies of Food for Thinking Christians and had them circulated by messenger boys. Small congregations grew up almost over night, but they remaind very small.
A significant number of early converts within the United States were immigrants from the UK. They evangelized by mail, and Russell notes that one of them wrote letters to put interested readers in England and Scotland in touch with each other. That in brief, is the story as two reliable historians present it. What the Watchtower says is mostly wrong.