Early research proposed that individuals with developmental dyslexia use contextual information to facilitate lexical access and compensate for phonological deficits. Yet at present there is no corroborating neuro-cognitive evidence. We explored this with a novel combination of magnetoencephalography (MEG), neural encoding and grey matter volume analyses. We analysed MEG data from 41 adult native Spanish speakers (14 with dyslexic symptoms) who passively listened to naturalistic sentences. We used multivariate Temporal Response Function analysis to capture online cortical tracking of both auditory (speech envelope) and contextual information. To compute contextual information tracking we used word-level Semantic Surprisal derived using a Transformer Neural Network language model. We related online information tracking to participants' reading scores and grey matter volumes within the reading-linked cortical network. We found that right hemisphere envelope tracking was related to better phonological decoding (pseudoword reading) for both groups, with dyslexic readers performing worse overall at this task. Consistently, grey matter volume in the superior temporal and bilateral inferior frontal areas increased with better envelope tracking abilities. Critically, for dyslexic readers only, stronger Semantic Surprisal tracking in the right hemisphere was related to better word reading. These findings further support the notion of a speech envelope tracking deficit in dyslexia and provide novel evidence for top-down semantic compensatory mechanisms.