This article explains how old, poor people living with dementia came to be institutionalised in 19th‐century Britain (with a focus on London), and how they were responded to by the people who ran those institutions. The institutions in question are lunatic asylums, workhouses and charitable homes. Old people with dementia were admitted to lunatic asylums, workhouses and charitable homes, but were not welcome there. Using the records of Hanwell lunatic asylum, published texts of psychiatric theory, and the administrative records that all of these institutions generated at local and national levels, this article argues that ‘the senile’ were a perpetual classificatory residuum in the bureaucracy of 19th‐century health and welfare. They were too weak and unresponsive to adhere to the norms of the asylum regime, yet too challenging in their behaviour to conform to that of the workhouse, or the charitable home. Across all of these institutions, old people with dementia were represented as an intractable burden, many decades before the ‘ageing society’ became a demographic reality.