Merton Council says plans to remove A&E and maternity from St Helier Hospital will cause the displacement.
The details, first proposed in 2019, would see the departments centralised at a proposed new hospital in Belmont in Sutton.
Epsom and St Helier NHS Trust says the move will ensure residents can access the care they need in facilities that are fit for purpose.
But Merton Council says the plans are outdated after the Covid pandemic.
People aged over 65 account for 42% of A & E attendances in South West London.