Abstract The development of recyclable crosslinked thermosetting fibres is a challenging research topic. In the present work, we have designed and synthesized polyurethane fibres from fructose‐derived 5‐chloromethylfurfural (CMF) and lignin‐derived monomeric phenols. The greenhouse gas emissions associated with the production of CMF showed comparable results to that of 5‐hydroxymethylfurfural (HMF), a high potential sugar‐based platform molecule. The wet‐spun biobased polyurethane fibres produced could be conveniently crosslinked using Diels–Alder chemistry to effectively enhance the glass transition temperature and mechanical properties. At a mildly elevated temperature (140 °C), the chemically crosslinked fibres could be effectively de‐crosslinked, which enabled complete separation from a mixture with poly(ethylene terephthalate) (PET) and cotton fibres. These results outline a potential strategy to design and fabricate new biobased fibres with reversible crosslinking, which may enable fibre‐to‐fibre recycling.