The answer to that is difficult. It has to do mainly with technological limitations and fluid dynamics.
In fact, you should ask about time to flank speed, as this would be your only measure of maximum output shaft horsepower (shafts, actually). The power delivered to the shaft is just enough to propel ship at desired speed. For example,
HMS Canada could cruise at 14 knots using less than 18% of nominal power, yet reaching 22 knots required her full (nominal) power of over 38k shp (303 RPM). And during trials she exceeded 24 knots, at 52.6k shp (and propeller shaft RPM exceeded 335). At those speeds water is... hard would be one way of putting it. Another is: when one goes that fast it's not a lubricant anymore...
See "British Battleships of World War One: New Revised Edition" for more details.
Another problem is cavitation, which was recognized well after 1960s, and which reduces the efficiency of powertrain.
And last but not least... With the exception of nuclear-powered ships designed from keel as such, ships designs are optimized for cruising speed (which is not the max speed), and those designs are not as efficient at high speeds. There are ways to alleviate that, but obviously older designs would be deficient in that regard, sometimes greatly. This has to do with fuel consumption, which is not a concern for nuclear-powered vessels. So while it's not in your question, I would recommend to do any comparison on era-by-era basis.
So. By now you should see the problem with your question...
Typically battleships of that size (25-30k tons displacement) required about 50-60 min to reach maximum speed. They could reach maximum power only during max-speed runs, as power produced by the engines must be dumped somewhere, and you literally can't run ship's propeller shaft from start to 330RPM in no-time. It's same thing everywhere - when you want to burn tyres when accelerating in your car there are parts of the transmission system that would prevent engine from sending all it's power to the powertrain... There is a reason why new (that is new when they first unveiled the new generation) Nissan GTR had a caveat in warranty stating pressing "race mode" button voids it as it is likely to damage shaft.
And the above numbers are nothing.
USS Iowa, when on her trials, reached contracted 32.5 knots, what requried about 212k shp. And she was running light for that. How long it took is nowhere to be found (those numbers are classified), but since she was larger than
Hood (and heavier) it would be definintely longer. For some basic info on British ships see here, for stats on
CVNs have on hand even more: Truman is rated for 31 knots at 280k shp from 8 nuclear reactors.
And one must not forget that
USS Iowa was built with designed overload of 20%, so we don't really know how fast really she could go. Same thing would apply to most WWII-era ships.
To show you how much power we're talking about
Queen Elizabeth 2 has, if I remember correctly, 2 power plants of output of 86MW each. I can barely imagine how much power that is, and yet it's most certainly not a patch on BB class. But even then this is a lot and even with modern designs one cannot use all that pile of power immediately.