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This paper analyses the effect of wealth inequality on UK economic growth in recent decades with a heterogeneous-agent growth model where agents can enhance individual productivity growth by allocating time to entrepreneurship. Entrepreneurship cost is negatively correlated to individual wealth which originates from the fact that the rich are more likely to undertake entrepreneurship than the poor. An appropriate wealth concentration to the rich theoretically stimulates their entrepreneurship incentives and then aggregate growth. Given UK quarterly data from 1978 to 2015, our model cannot be rejected to be true using the Indirect Inference method. The empirical study finds that our structural model could generate a stable relation between inequality and growth and model simulations could fit main properties of UK economy. Wealth inequality is found to stimulate economic growth, especially in a long term. Policy makers have to face a trade-off when conduct a redistribution policy like taxation because inequality reduction will be followed by a slow-down of economic growth. Moreover, as redistribution tax rate increases, growth reduction has a gradiently increasing trend and thus a moderate tax rate is a priority option for policy makers. Our comparison between tax regimes shows that the tax transferring income from the rich to the poor is preferred to others.