The present invention relates to a composition for dyeing keratin fibres, comprising: one or more oxidation dyes; one or more basifying agents; one or more non-oxyalkylenated fatty substances that are liquid at room temperature in a content of less than or equal to 20% by weight relative to the total weight of the composition; one or more oxidizing agents; one or more oxyethylenated fatty alcohols with a number of oxyethylene units of greater than or equal to 10; one or more oxyethylenated fatty alcohols with a number of oxyethylene units of less than 10; one or more non-oxyethylenated fatty alcohols that are solid at room temperature; and one or more cationic polymers. The present invention also relates to a process for dyeing keratin fibres using such a composition, and also to a kit for preparing the said composition.