Identical genetic variations can have different phenotypic effects depending on their parent of origin. Yet, studies focusing on parent-of-origin effects have been limited in terms of sample size due to the lack of parental genomes or known genealogies. We propose a probabilistic approach to infer the parent-of-origin of individual alleles that does not require parental genomes nor prior knowledge of genealogy. Our model uses Identity-By-Descent sharing with second- and third-degree relatives to assign alleles to parental groups and leverages chromosome X data in males to distinguish maternal from paternal groups. We combine this with robust haplotype inference and haploid imputation to infer the parent-of-origin for 26,393 UK Biobank individuals. We screen 99 phenotypes for parent-of-origin effects and replicate the discoveries of 6 GWAS studies, confirming signals on body mass index, type 2 diabetes, standing height and multiple blood biomarkers, including the known maternal effect at the MEG3/DLK1 locus on platelet phenotypes. We also report a novel maternal effect at the TERT gene on telomere length, thereby providing new insights on the heritability of this phenotype. All our summary statistics are publicly available to help the community to better characterize the molecular mechanisms leading to parent-of-origin effects and their implications for human health.