I suspect that the podcast may be referring to published research by Robert Allen of Oxford University. In his 2006 paper Explaining The British Industrial Revolution From the Perspective of Global Wage and Price History. Professor Allen observes:
In Britain, wages were remarkably high and energy cheap. This wage and price history was a fundamental reason for the technological breakthroughs of the eighteenth century whose object was to substitute capital and energy for labour.
He goes on to note that:
Scientific discoveries and scientific culture do not explain why Britain differed from the rest of Europe. They may have been necessary conditions for the industrial revolution, but they were not sufficient: Without Britain’s distinctive wage and price environment, Newton would have produced as little economic progress in England as Galileo produced in Italy
However, Professor Allen does not seem to be claiming that high wages were a single root cause of the Industrial Revolution. Indeed, in another paper from 2006, The High Wage Economy of Pre-industrial Britain, he notes that England was not unique in having a high-wage economy in the eighteenth century. A similar situation existed in the Low Countries:
England and the Low Countries stood out in the eighteenth century for their high wage economies. At the exchange rates, wages were higher in northwestern Europe than elsewhere.
This did not impact their trading positions however, since:
English and Dutch industries were highly competitive internationally, their productivity must also have been high.
Wages were not just higher in England and the Low Countries than they were in the rest of Europe. They were also relatively high compared to the cost of living:
English and Dutch wages were also high relative to the cost of living. In most of continental Europe and Asia in the eighteenth century, a labourer’s wage was just enough to keep his family at bare bones subsistence. In contrast, labourers in England and the Netherlands could afford a diet with meat, beer, and cheese and still have a little left over to buy the odd luxury.
Professor Allen also claims that this high-wage economy created a stimulus for the Industrial Revolution by priming a "consumer revolution" which generated a market for many the products produced by the Industrial Revolution:
In addition, these favoured workers had money to buy novel and exotic consumer goods. They were an important part of the ‘consumer revolution’ that provided a mass market for non-traditional goods that prompted much product innovation in English manufacturing.
Clearly therefore, the implication is that the high wages were an important factor in triggering the Industrial Revolution in England, but not the only one.
EDIT
It is worth noting the following observation in regard to Robert Allen's hypothesis, made by @FranzPlumpton in the comments below:
But note that the so-called HWE-hypothesis as a cause for the BIR is slowly falling apart. People have been showing that his wages series were mismeasured (e.g. Judy Stephenson), furthermore his reference point of Italy was underestimated (e.g. Malanima shows that wages in Italy were higher than previously thought, as high as in ENG), wages in France were similarly high (e.g. Vincent Geloso for Straßburg). Then there is Humphries and her update on female wages. Plus she and Weisdorf have a new paper that also contradict Allen (more in support of an industrious revolution à la Jan de Vries)
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