This is a tricky question to answer because there are really two parts to the question.

A) Was Ireland deforested during a period of British rule? Yes. More of the deforestation-though Irish native species had already been on a decline since the last Ice Age-occurred from the 1600s, with increased demand for agricultural land resulting in the felling of trees, to the 1700s and 1800s, when demand for charcoal, one of the predominant fuel sources of Northwest Europe (alongside peat) began to skyrocket and woods began to disappear in Ireland and England to satisfy the burning (couldn't resist, sorry) desire for cheap energy.

B) Was this forestry the fault of the British Crown? Questionable, but I would tend towards the negative. The English government, if anything, understood the risk of allowing prospectors free reign on woods, having seen its own supply of cheap fuel shrink dramatically in the 1600s and instituting crown protections on forests as a consequence. The English government specifically allocated woods for certain types of industry-cannon smelting being one notable example-in an effort to preserve the renewable resource for strategic purposes. The English also changed the methods of extracting wood for energy generation-rather than just cutting down trees, the gathering of wood debris and branches was encouraged instead, allowing the "stock" to be replenished rather than just cutting the tree down.

That being said, the English crown had less than perfect control over its settlers in Ireland, which in some respects had aspects of the Wild West. The English crown was also perpetually short of money, and on numerous occasions the crown forests were sold to prospectors for their personal exploitation, which was not exactly helpful to forest conservation efforts. But what is important to note is that the consumption of these wood products was local: namely, that rather than Irish wood being shipped to England for consumption there (which would usually be considered "resource exploitation") it was Irish woodland being chopped down for Irish farmland and wood burned for Irish furnaces. Granted, much of this was for the benefit of English colonists (as well as Irish natives), but then we start to get into a topic of political identity that I will sidestep for sanity's sake.

The short and long of it is, as the population of Ireland grew (from natural growth and immigration), its demand for natural resources-both food and energy-grew accordingly, and the woodland of Ireland paid the price. While the English government did introduce regulations and protections on the lands, their ability to enforce the regulations-not to mention their willpower-was questionable at best.

Source: Everett, Nigel, The Woods of Ireland