Understanding genetic variants effects on the epigenome is crucial for interpreting genome-wide association studies (GWAS) results, yet profiling these effects across the non-coding genome remains challenging due to the scalability limits of experimental methods. This necessitates accurate computational models. Existing machine learning approaches, while progressively improving, are confined to the cell types they were trained on, limiting their applicability. Here, we propose the development of a deep learning model, Enformer Celltyping, which can both incorporate distal effects of DNA interactions, up to 100,000 base-pairs away, and predict epigenetic signals in a cell type-agnostic fashion. We demonstrate that Enformer Celltypings predictions of the epigenome out-perform the current best-in-class approach, have strong performance in a range of different cell types and biological regions and generalise to cell types assayed independently of the original training set. Finally, we propose an approach to test epigenetic models performance on genetic variant effect predictions using regulatory quantitative trait loci mapping studies, highlighting Enformer Celltypings and other genomic deep learning models limitations for this task. Our work introduces a new, accurate model for cell type-agnostic histone mark predictions and highlights the benefit of transfer learning for more efficient model development for deep learning in genomics. We make our customisable and efficient transfer learning approach for Enformer available to the community.