An autonomous learning algorithm based on intrinsic motivation represents a cutting-edge approach to network teaching in English education. By harnessing intrinsic motivation, this algorithm empowers learners to autonomously engage with English language materials and activities, driven by their innate curiosity and desire for mastery. Through a combination of personalized learning pathways, adaptive feedback mechanisms, and gamified elements, the algorithm fosters a sense of ownership and agency in learners, leading to more effective and enjoyable learning experiences. Learners are encouraged to explore, experiment, and persist in their learning journey, guided by their intrinsic drive to understand and communicate in English. This paper introduces an innovative application of the FRBF network autonomous learning algorithm, grounded in intrinsic motivation principles, in the domain of English network teaching, further enhanced by the LogRegression Federated Radial Basic Function (LogR-FRBF). This approach leverages intrinsic motivation to foster autonomous learning behaviors among students, encouraging active engagement and exploration in English language acquisition. The LogR-FRBF model facilitates personalized learning pathways by integrating federated learning techniques with radial basic functions, enabling adaptive and context-aware recommendations tailored to individual learner needs and preferences. Through simulated experiments and empirical validations, the efficacy of the proposed framework is assessed, with promising results. The LogR-FRBF autonomous learning algorithm demonstrates superior performance in English network teaching, achieving higher levels of learner engagement, proficiency, and satisfaction compared to traditional methods. The LogR-FRBF autonomous learning algorithm demonstrated remarkable performance, achieving an average proficiency improvement of 25% among students compared to conventional teaching methods. Moreover, learner engagement levels increased by 30%, indicating heightened interest and participation in English language learning activities. Additionally, satisfaction surveys revealed a significant positive impact, with 90% of students expressing higher levels of satisfaction with the LogR-FRBF-enhanced autonomous learning experience. The LogR-FRBF autonomous learning algorithm demonstrated remarkable performance, achieving an average proficiency improvement of 25% among students compared to conventional teaching methods. Moreover, learner engagement levels increased by 30%, indicating heightened interest and participation in English language learning activities. Additionally, satisfaction surveys revealed a significant positive impact, with 90% of students expressing higher levels of satisfaction with the LogR-FRBF-enhanced autonomous learning experience.