Promoting entrepreneurial activities is crucial for regions to facilitate innovation and economic development. Yet, becoming an entrepreneur is not aspired by all people, and regions may differ considerably in their entrepreneurship potential. Assessing and providing accurate estimates of the entrepreneurship potential across fine-grained spatial scales is thus crucial to inform regional policymakers, but it still remains a major challenge due to data availability. Here we used the lab data set from the British Broadcasting Corporation (BBC) covering 368,364 individuals and providing high-resolution data about their residences to map the entrepreneurship potential across 9271 postcode sectors in Great Britain. We used a novel mapping approach that relies on a spatial smoothing function based on distance weights to utilize the most fine-grained spatial level available in the data. Our detailed maps show substantial difference in entrepreneurship potential across postcode sectors in Great Britain and within the largest cities: London, Birmingham and Manchester.