Nelson and Rodney as a British treaty condition

Did Britain simply ask the other powers for permission to build Nelson and Rodney?

No. Britain made the right to build two new 16-inch battleships a condition of signing the treaty.

The distinction changes how treaty bargaining should be understood. Britain entered the talks with a large but older 15-inch fleet. It refused to accept a settlement that left it without a new 16-inch class while other powers retained their latest ships. Nelson and Rodney were therefore part of the price of British agreement, not a discretionary concession after the main bargain.