A landlord cannot pass ground rent on to his tenants, because he is already charging the maximum they will pay. If the landlord could raise prices even more, then he would already have done so!
So low-rise renting will decline, as it becomes less profitable. But high-rise renting will increase, because ground rent does not increase if you build extra floors. And with no taxes on work or goods, building extra floors is cheap, and renting them out is pure profit.
And if you grow tired of renting, ground rent means buying is much cheaper than before. With this increased supply, market rents for tenants must go down.