Mendelian Randomisation (MR) is an increasingly popular approach that estimates the causal effect of risk factors on complex human traits. While it has seen several extensions that relax its basic assumptions, most suffer from two major limitations; their under-exploitation of genome-wide markers, and sensitivity to the presence of a heritable confounder of the exposure-outcome relationship. To overcome these limitations, we propose a Latent Heritable Confounder MR (LHC-MR) method applicable to association summary statistics, which estimates bi-directional causal effects, direct heritabilities, and confounder effects while accounting for sample overlap. We demonstrate that LHC-MR outperforms several existing MR methods in a wide range of simulation settings and apply it to summary statistics of 13 complex traits. Besides several concordant results with other MR methods, LHC-MR unravels new mechanisms (how disease diagnosis might lead to improved lifestyle) and reveals new causal effects (e.g. HDL cholesterol being protective against high systolic blood pressure), hidden from standard MR methods due to a heritable confounder of opposite effect direction.