The Internet of Things (IoT) consists of millions of devices deployed over hundreds of thousands of different networks, providing an ever-expanding resource to improve our understanding of and interactions with the physical world. Global service discovery is key to realizing the opportunities of the IoT, spanning disparate networks and technologies to enable the sharing, discovery, and utilisation of services and data outside of the context in which they are deployed. In this paper, we present Decentralised Service Registries (DSRs), a novel trustworthy decentralised approach to global IoT service discovery and interaction, building on DSF-IoT to allow users to simply create and share public and private service registries, to register and query for relevant services, and to access both current and historical data published by the services they discover. In DSR, services are registered and discovered using signed objects that are cryptographically associated with the registry service, linked into a signature chain, and stored and queried for using a novel verifiable DHT overlay. In contrast to existing centralised and decentralised approaches, DSRs decouple registries from supporting infrastructure, provide privacy and multi-tenancy, and support the verification of registry entries and history, service information, and published data to mitigate risks of service impersonation or the alteration of data. This decentralised approach is demonstrated through the creation and use of a DSR to register and search for real-world IoT devices and their data as well as qualified using a scalable cluster-based testbench for the high-fidelity emulation of peer-to-peer applications. DSRs are evaluated against existing approaches, demonstrating the novelty and utility of DSR to address key IoT challenges and enable the sharing, discovery, and use of IoT services.