Whole-genome sequencing (WGS) is becoming widely used in clinical medicine in diagnostic contexts and to inform treatment choice. Here we evaluate the potential of the Oxford Nanopore Technologies (ONT) MinION long-read sequencer for routine WGS by sequencing the reference sample NA12878 and the genome of an individual with ataxia-pancytopenia syndrome and severe immune dysregulation. We develop and apply a novel reference panel-free analytical method to infer and then exploit phase information which improves single-nucleotide variant (SNV) calling performance from otherwise modest levels. In the clinical sample, we identify and directly phase two non-synonymous de novo variants in SAMD9L, (OMIM #159550) inferring that they lie on the same paternal haplotype. Whilst consensus SNV-calling error rates from ONT data remain substantially higher than those from short-read methods, we demonstrate the substantial benefits of analytical innovation. Ongoing improvements to base-calling and SNV-calling methodology must continue for nanopore sequencing to establish itself as a primary method for clinical WGS.