How much responsibility did this reconfiguration of the English legal system enable the birth and widespread economic and global success of the British Empire that followed on its heels?

One would not necessarily connect the two but in fact there is an interrelationship. There were many machinations of British society that resulted from the new legal perspectives governing things, and this created a number of opportunities for lateral as well as upward mobility of human individuals within society and the creation of a much larger military and navy than possible previously through coercion alone, and this was seen to be a win-win by the rulers of the era, that they could use their wealth to obtain cooperation of their minions and this, in turn, extended their reach and consolidated power in a way that was more stable than ever before because there was less infighting and episodes of insurrection by disaffected individuals who could get a conspiracy going and foment trouble. If you think about this, it is quite logical that a just legal system creates, through establishing order, a greater economic stability and potential for growth and prospering of society. Even if it is done through the ruling of a royal dynasty rather than a democracy, it is a stepping stone to the betterment of the individual and creates the potential leading directly to democratic governance and greater individual freedom overall. So this has been a steady progression of growing freedom in alignment with greater expression of human divinity as achieved through divine intervention and support.