Why modern Britain is not the same legal entity

The legal entity that participated in the slave trade was the British Crown and its colonial administration as they existed in the seventeenth and eighteenth centuries. That entity operated under a constitutional framework that has been transformed beyond recognition in the intervening centuries. Parliamentary sovereignty, the scope of executive power, the legal rights of individuals, the constitutional relationship between Britain and its territories, all of these have changed fundamentally.

Whether the modern British state is the legal successor of the colonial state in a way that carries specific financial liabilities from the slave trade era is a genuinely open legal question. It is not the obvious yes that reparations advocates imply. International law does not provide a clear answer, and domestic British courts would be unlikely to accept jurisdiction over such a claim in any case.