In recent years, an increasing number of English teachers have recognized the importance of reading and writing skills. Traditional English teaching methods often overlook the essential link between these skills, which hinders the improvement of students’ overall English proficiency. This paper introduces an adaptive Huber growth curve model to represent cognitive abilities in English reading. It develops an English reading ability detection model using a function-based approach. The model involves word feature extraction, fine-grained learning, and establishing information channels. These processes collectively contribute to a sequence annotation model that not only identifies but also automatically corrects errors in English writing samples. This facilitates integrated intelligent teaching of reading and writing skills. Analysis of English reading and writing capabilities among students at various colleges and universities reveals that the most notable improvement is in students’ critical thinking abilities during English reading, with most scores ranging between 3.5 and 4 and a total of 52 students participating. The difference in writing scores of the subject classes was 1.4186, of which the T value was 3.7855, the DF value was 112.3, and the P value was 0.000, which was significant, and the magnitude of the English writing scores of the subject class A was greater than that of the class B, which indicated that the integration of literacy and writing effectively improved the overall writing skills of the students.