Reference panels from the 1000 Genomes (1000G) Project Consortium provide near complete coverage of common and low-frequency genetic variation with minor allele frequency >= 0.5% across European ancestry populations. Within the European Network for Genetic and Genomic Epidemiology (ENGAGE) Consortium, we have undertaken the first large-scale meta-analysis of genome-wide association studies (GWAS), supplemented by 1000G imputation, for four quantitative glycaemic and obesity-related traits, in up to 87,048 individuals of European ancestry. We identified two loci for body mass index (BMI) at genome-wide significance, and two for fasting glucose (FG), none of which has been previously reported in larger meta-analysis efforts to combine GWAS of European ancestry. Through conditional analysis, we also detected multiple distinct signals of association mapping to established loci for waist-hip ratio adjusted for BMI (RSPO3) and FG (GCK and G6PC2). The index variant for one association signal at the G6PC2 locus is a low-frequency coding allele, H177Y, which has recently been demonstrated to have a functional role in glucose regulation. Fine-mapping analyses revealed that the non-coding variants most likely to drive association signals at established and novel loci were enriched for overlap with enhancer elements, which for FG mapped to promoter and transcription factor binding sites in pancreatic islets, in particular. Our study demonstrates that 1000G imputation and genetic fine-mapping of common and low-frequency variant association signals at GWAS loci, integrated with genomic annotation in relevant tissues, can provide insight into the functional and regulatory mechanisms through which their effects on glycaemic and obesity-related traits are mediated.