In this paper, we examined the association among the energy sector stock, oil prices and stock market on the whole. We also considered the UK position from the net oil exporter to net oil importer and implications of the Global Financial Crises. Employing a Time-Varying Vector Auto-regressive framework on monthly data from January 1990 to June 2015 in which the sources of time variation were both the coefficients and variance-covariance matrix of the innovations, this study found that historically oil price shocks have negatively affected the stock market, however the energy sector stock has always responded positively holding their title as hedge against oil shocks. It was also found that the shift from net oil exporter to net oil importer did not influence the association between the UK stock market and oil shocks much. Including the discrete break and subsampling of series led to controlling for the prior beliefs and agent's behaviour in the Pre-GFC period. It turned out that the GFC had been a game changer and the stock market as well as the energy sector showed a positive and symmetric response to oil shocks. These findings have profound implications in terms of depressed global aggregate demand and oil shocks dynamics in the Post-GFC world.