A naval war removes peacetime funding restraints

Would the Royal Navy receive funding for modern battleships during and after this Pacific war?

Yes; an active naval war would override many treaty and Treasury restraints and give the Navy priority over competing service demands.

A war centred on fleets would give the Royal Navy unusually strong claims on national resources. Treaty-based objections and Treasury resistance would lose force once Britain was actually fighting a naval war. The Navy would also compete less intensely with the other services than it did during a land-and-air war in Europe. Modern battleships and supporting construction therefore become politically easier, although the precise designs still depend on combat experience.