<b><i>Background:</i></b> Previous analyses have identified common variants along with some specific genes and rare variants which are associated with risk of hypertension, but much remains to be discovered. <b><i>Methods and Results:</i></b> Exome-sequenced UK Biobank participants were phenotyped based on having a diagnosis of hypertension or taking anti-hypertensive medication to produce a sample of 66,123 cases and 134,504 controls. Variants with minor allele frequency (MAF) <0.01 were subjected to a gene-wise weighted burden analysis, with higher weights assigned to variants which are rarer and/or predicted to have more severe effects. Of 20,384 genes analysed, 2 genes were exome-wide significant, <i>DNMT3A</i> and <i>FES</i>. Also strongly implicated were <i>GUCY1A1</i> and <i>GUCY1B1</i>, which code for the subunits of soluble guanylate cyclase. There was further support for the previously reported effects of variants in <i>NPR1</i> and protective effects of variants in <i>DBH</i>. An inframe deletion in <i>CACNA1D</i> with MAF = 0.005, rs72556363, is associated with modestly increased risk of hypertension. Other biologically plausible genes highlighted consist of <i>CSK</i>, <i>AGTR1</i>, <i>ZYX</i>, and <i>PREP</i>. All variants implicated were rare, and cumulatively they are not predicted to make a large contribution to the population risk of hypertension. <b><i>Conclusions:</i></b> This approach confirms and clarifies previously reported findings and also offers novel insights into biological processes influencing hypertension risk, potentially facilitating the development of improved therapeutic interventions. This research has been conducted using the UK Biobank Resource.