There's a lot more to this, but Pomeranz argues that Britain's industrial revolution would have been unsustainable without the 'ghost acres' acquired through colonisation, which enabled Britain to continue to consume. That might be a good starting point for you.

Kenneth Pomeranz, The Great Divergence (2000)

It's more something (as I understand) that economic historians argue about. Groups that look at demography, for example the 'California Group'. The so-called 'Financial Revolution' is a pretty important part of this debate, as the building up of banking and credit institutions is seen to have enabled expansive and dynamic Dutch and British trading empires in various centuries.

To return to your question, they are completely and absolutely related- and too intertwined to argue causality, though some people have. I haven't studied this for years and undoubtedly there are more expert people. One part of the argument is the debate over the starting point of the industrial revolution. Some people- such as Belich- argue that the plague of the fourteenth century was key in kicking off the path that led Western Europe towards an indusrial revolution, rather than, say, China.

Ultimately I'd say that the Industrial Revolution came first, if only because this had absolutely already happened by the time that Britain's became the largest empire. Remember that for centuries Britain's empire was smaller than that of the Iberian countries, the Dutch, the Chinese, The Ottomans... I realise that you're specifically thinking about colonial empire- but perhaps check a map of the growth of this. Many colonies were acquired (surprisingly?) late: the 'scramble for Africa' was only in the later nineteenth century.