York is among the 100 worst-hit areas of the country, according to analysis by the Energy and Climate Intelligence Unit (ECIU).
It shows that of the 12,699 privately rented homes in the York Central constituency, 6,946 have an Energy Performance Certificate (EPC) rating of D or lower.
Plans to ensure all new tenancies must meet EPC band C by 2025 were scrapped by Mr Sunak in September.
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