Mendelian Randomisation (MR), an increasingly popular method that estimates the causal effects of risk factors on complex human traits, has seen several extensions that relax its basic assumptions. However, most of these extensions 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 heritability, 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, LHC-MR unravelled new mechanisms (how being diagnosed for certain diseases might lead to improved lifestyle) and revealed potential false positive findings of standard MR methods (apparent causal effect of body mass index on educational attainment may be driven by a strong ignored confounder). Phenome-wide search to identify LHC-implied heritable confounders showed remarkable agreement between the LHC-estimated causal effects of the latent confounder and those for the potentially identified ones. Finally, LHC-MR naturally decomposes genetic correlation to causal effect-driven and confounder-driven contributions, demonstrating that the genetic correlation between systolic blood pressure and diabetes is predominantly confounder-driven.