Genotype-environment interaction (G×E) studies typically focus on variants with previously known marginal associations. While such two-step filtering greatly reduces the multiple testing burden, it can miss loci with pronounced G×E effects, which tend to have weaker marginal associations. To test for G×E effects on a genome-wide scale whilst leveraging information from marginal associations in a flexible manner, we combine the conditional false discovery rate with interaction test results obtained from StructLMM. After validating our approach, we applied this strategy to UK Biobank (UKBB) data to probe for G×E effects on BMI. Using 126,077 UKBB individuals for discovery, we identified known (FTO, MC4R, SEC16B) and novel G×E signals, many of which replicated (FAM150B/ALKAL2,TMEM18, EFR3B, FAIM2, UNC79, LAT) in an independent subset of UKBB (n=126,076). Finally, when analysing the full UKBB cohort, we identified 140 candidate loci with G×E effects, highlighting the advantages of our approach.