Cross-modal hashing has attracted widespread attention from researchers due to its capabilities to handle large volumes of heterogeneous multimedia information with fast retrieval speed and low storage cost. However, current cross-modal hashing methods still face issues such as incomplete embedding of semantic correlation information and long parameter tuning cycles. To address these problems, we propose a method called Unsupervised Adaptive Hypergraph Correlation Hashing (UAHCH). First, the hypergraph-based correlation enhanced hashing constructs a hypergraph based on semantic information and correlation information, leveraging a hypergraph neural network to integrate the hypergraph information into the hash codes, ensuring the richness of the semantics and the integrity of correlation relationships. Next, the fast parameter adaptive strategy is designed for the automated optimization of neural network parameters for the UAHCH method and various neural network models, achieving optimal performance more efficiently. Finally, comprehensive experiments are conducted on widely used datasets. The results show that the proposed UAHCH method achieves superior performance, with average improvements of 3.06% on MIRFlickr, 1.45% on NUS-WIDE, and 4.65% on MSCOCO compared to the latest baseline methods. The code has been made publicly available at https://github.com/YunfeiChenMY/UAHCH.