A negative-working heat-sensitive material for making a lithographic printing plate by direct-to-plate recording is disclosed. The material comprises in the order given a lithographic base having a hydrophilic surface, an oleophilic imaging layer and a cross-linked hydrophilic upper layer which comprises an organic compound derived from sulfonic acid, sulfuric acid, phosphoric acid or phosphonic acid. Materials according to the invention are characterized by an increased water-acceptance in the non-printing areas, which allows a rapid start-up of the press.