State-of-the-art deep learning entity linking methods rely on extensive human-labelled data, which is costly to acquire. Current datasets are limited in size, leading to inadequate coverage of biomedical concepts and diminished performance when applied to new data. In this work, we propose to automatically generate data to create large-scale training datasets, which allows the exploration of approaches originally developed for the task of extreme multi-label ranking in the biomedical entity linking task. We propose the hybrid X-Linker pipeline that includes different modules to link disease and chemical entity mentions to concepts in the MEDIC and the CTD-Chemical vocabularies, respectively. X-Linker was evaluated on several biomedical datasets: BC5CDR-Disease, BioRED-Disease, NCBI-Disease, BC5CDR-Chemical, BioRED-Chemical, and NLM-Chem, achieving top-1 accuracies of 0.8307, 0.7969, 0.8271, 0.9511, 0.9248, and 0.7895, respectively. X-Linker demonstrated superior performance in three datasets: BC5CDR-Disease, NCBI-Disease, and BioRED-Chemical. In contrast, SapBERT outperformed X-Linker in the remaining three datasets. Both models rely only on the mention string for their operations. The source code of X-Linker and its associated data are publicly available for performing biomedical entity linking without requiring pre-labelled entities with identifiers from specific knowledge organization systems.