“Tokyo ESP Gaiden” London ESP has now been fully translated. The translated volume is being hosted at my branch site, Tokyo ESP Scans, with 6 chapter in total, including the prologue and epilogue. You can find the table of contents here.
London ESP is a digital light novel that is published for free by several ebook stores, including Bookwalker. About the story, it revolves around Minami and Kozuki who went missing after the Great Liberation incident at Tokyo Skytree. So it would only make sense if the readers have followed the original manga up to that scene before going into this branch novel.