No Earth connected to property I am renting. Plug burnt and I noticed the earth did not trip

No, it is not legal to rent out a property with no earth connection. Under the Electrical Safety Standards in the Private Rented Sector (England) Regulations 2020, landlords must ensure that the electrical installation is safe and complies with BS 7671 (IET Wiring Regulations). A missing earth connection is a serious safety defect and would fail an Electrical Installation Condition Report (EICR). Ignoring known safety issues or tenant complaints may also breach the Housing Act 2004, which can lead to enforcement action by the local authority.