Instructor-recommended websites that focus on building reading skills:

$ AceReader: Designed for mainstream learners but is also successfully used by English-language learners. More than 1,000 reading comprehension tests that are themed and levelled. Each time a test is taken, learners’ speed and comprehension scores are logged. Learners can monitor their own progress, and instructors can track their results. https://www.acereader.com/education

Breaking News English (British): The lessons are based on world current events, produced twice weekly, with levels ranging from 0–7. The 0 level corresponds to CEFR2 (the Common European Framework of Reference for Languages, high basic level). The lessons include a downloadable PDF, a two-page mini lesson and podcasts delivered in British or American accents. The online activities provide a variety of skills practice: reading at different speeds, grammar activities and vocabulary flashcards, gap fill and matching games.
http://www.breakingnewsenglish.com/

English Zone Reading (American): This site offers basic reading activities with text in three levels: easy, intermediate and advanced. Topics range from animals, to clothing labels, map reading and health problems. Each reading comes with a quiz with a drop-down menu. The website also contains activities for grammar, idioms, verbs and spelling, plus teacher resources. http://www.english-zone.com/reading/