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There is currently considerable excitement within government about the potential of artificial intelligence to improve public service productivity through the automation of complex but repetitive bureaucratic tasks, freeing up the time of skilled staff. Here, we explore the size of this opportunity, by mapping out the scale of citizen-facing bureaucratic decision-making procedures within UK central government, and measuring their potential for AI-driven automation. We estimate that UK central government conducts approximately one billion citizen-facing transactions per year in the provision of around 400 services, of which approximately 143 million are complex repetitive transactions. We estimate that 84% of these complex transactions are highly automatable, representing a huge potential opportunity: saving even an average of just one minute per complex transaction would save the equivalent of approximately 1,200 person-years of work every year. We also develop a model to estimate the volume of transactions a government service undertakes, providing a way for government to avoid conducting time consuming transaction volume measurements. Finally, we find that there is high turnover in the types of services government provide, meaning that automation efforts should focus on general procedures rather than services themselves which are likely to evolve over time. Overall, our work presents a novel perspective on the structure and functioning of modern government, and how it might evolve in the age of artificial intelligence.