The City of London allows corporations to vote because its existence as local authority predates anything else that exists in the UK. Mentions of The City of London's special rights exist in the Magna Carta, and it was never included in any of the local authority voting reforms the occurred since its creation.

The local population number have absolutely nothing to do with the existence of corporate votes in The City of London. It's not even the smallest local authority by population, the Isles of Scilly are, and corporations have no votes there.