Very true. HMS Victory required something like 6,000 mature oak trees to build, exclusive of the softwoods used for its decks and masts, and it was only one of close to 100 ships of the line in commission around say 1800. (To be fair, many of those ships had been captured from France or Spain, but there were also many smaller ships in commission.)

By the end of the Napoleonic wars, the British were importing timber from everywhere they could get it, and building in overseas yards (India and the Americas). I wrote more about this here: https://www.reddit.com/r/AskHistorians/comments/27ye2f/did_the_royal_navy_build_all_its_ships_in_britain

If you read old town charters in New England the best wood is set aside for the Royal Navy, especially the tallest and straightest pines.

The book Coal, A Human History, by Barbara Freese, puts the overall blame for deforestation of England on the need for fuel. She says that in the 15th century England had just about no navy, and that deforestation in the 16th started the massive conversion from wood as fuel to coal as fuel. She also points out that transportation of heavy loads of coal on what passed for roads in England at that time was near impossible, so very many ships were built to carry the coal from Newcastle to London. She credits this large amount of shipping and the resulting maritime know-how as a significant contributor to England's ascendancy as a naval and trading power.