Relationship between deforestation and industrialization?

(I have no background in any relevant field.) There’s definitely a ton of evidence that industrialization leads to deforestation, at least under common conditions. (And there are probably some ways that industrialization reduces deforestation.)

But I’m wondering whether there are any prominent scholarly arguments that deforestation contributed to industrialization, especially in Britain.

The reason that this occurred to me is the following:
1. I think I’ve read in various places that Britain was an outlier in terms of deforestation in the early modern period. I remember not being sure about the evidence I was looking at, since different bits of forest have different kinds of possible human uses.
2. I’ve definitely read in various places that Britain’s early start on its modern phase of industrialization could be partially explained by “relative factor prices,” in particular
a. Availability of cheap coal
b. Availability of cheap labor of certain types (children, women, dispossessed farmers to work in early factories and other “intensely managed” production situations)
c. Scarcity of cheap labor of certain types (thinking of Robert Allen’s arguments based on reconstructed wage data).

If #1 is accurate, then I was wondering whether anyone has added a part d (“scarcity of cheap wood”) to #2.