Which was a HILARIOUS episode of Have I Got News For You
In the 1990s, Angus Deaton noted that the CPI we use to deflate tend to be based on weights for people in the top quartile of the population income-wise. When you shift to weights that represent poor people's expenditure patterns, you find different rates of inflation.
For the end of the 1860s to the 1910s, this was not trivial. The poor had more deflation (yes) than the "usual CPI" (and far more than the rich). Thus, just for these reasons, we understate their gains. Below I show the hourly wages of production workers deflated by either the CPI or a poor-people price index. You miss a great deal of gains.
Over that period, it means that the real gains at 2.5% per annum compared to 2.11% per annum. A 0.4 pp difference which is huge. So the faster-growing series cuts the time needed for wages to double by roughly 5 years (28 years instead of 33 years)