This dataset contains detailed supplementary quality assessment tables supporting a systematic review of the respiratory health impacts of cold homes, housing energy efficiency, and heating interventions. Provided in Microsoft Word format, these tables present the granular Risk of Bias (RoB) ratings for the 35 studies included in the review, broken down by individual bias domains and overall global assessment. The quality appraisal utilised three standard tools, tailored to the specific study designs: ROBINS-E for observational studies of exposures (implementing a modified approach for assessing confounding bias developed for this project), ROBINS-I for non-randomised interventional studies, and RoB-2 for randomised controlled trials. All assessments were conducted independently by two reviewers (Isobel Braithwaite and Nazanin Rassa), with disagreements resolved through consensus.This review was conducted as part of the PhD thesis "Housing Energy Efficiency and Health: A National Longitudinal Data Linkage Study" (University College London, submitted September 2025). The wider research project aimed to clarify the complex relationship between cold housing, energy efficiency measures, and common respiratory health conditions to better inform public health and housing policy. A peer-reviewed paper based on the findings of this systematic review is currently in preparation.