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This source may help you β UK Data Service: London weekly bills of mortality, 1644β1849
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In the paper "Patterns of smallpox mortality in London, England, over three centuries" authors deal with exactly this problem:
We accessed original documents in London, England, in the Guildhall Library, the British Library, the Wellcome Library, and the London Metropolitan Archive. We digitized weekly reported birth and death records for London throughout the period over which smallpox was listed as a cause of death (1661 to 1934). The last smallpox death reported in London was in the week beginning 17 February 1934. The last year when more than one smallpox death was reported in a single week was 1930, so we do not present data or analyses after 1930 (in total, only 7 smallpox deaths were reported from 1931 to 1934).
All data are available at GitHub.