Where the landlord is liable to pay any . . . rates (including water rate) in respect of any premises comprised in a holding, or has undertaken to pay the premiums on any fire insurance policy on any such premises, and in consequence of any improvement executed by the tenant on the premises under this Act the assessment of the premises or the rate of premium on the policy is increased, the tenant shall be liable to pay to the landlord sums equal to the amount by which—
the . . . rates payable by the landlord are increased by reason of the increase of such assessment;
the fire premium payable by the landlord is increased by reason of the increase in the rate of premium;
and the sums so payable by the tenant shall be deemed to be in the nature of rent and shall be recoverable as such from the tenant, . . .