Since Britain had northest US as colonys, that became their supply of Oak when they ran out of Oak forests.

Not even that much. Britain was heavily forested originally, so there was plenty of timber to be found in England to make the huge fleets. The British ran out of forests during the Industrial Revolution. Before they started digging for coal to power their machinery and keep the steel mills furnaces running, they cut down the British forests.

Mind you, both the Dutch and the British had far easier acces to shipping timber through trading with the Baltic, for backup. Spain was far less forested than either of those two countries. In the beginning this didn’t matter all that much since the original ships from the Columbian era were really, really tiny. But about a century later, far larger fleets of ships five or six times bigger were required for both warfare and long-range trade. Spain’s forests couldn’t support that.