When you get right down to it, few plastic ship model kits have really good painting instructions. Some are much better than others, of course, but mighty few give the authentic color names and show exactly where each color goes.
Many times the color guides are just plain wrong. Many more times, the colors indicated are about right, but when it comes to naming them all you get is a number that corresponds with a particular manufacturer's paint line. (Revell Germany, for instance, makes some really fine ship kits, but the colors are only identified by Revell paint numbers. And I've never seen Revell paints in an American hobby shop.)
In this particular case, the problem is compounded by the fact that there are few model paint colors that are matched exactly to British Royal Navy colors. The only ones I know of are the Colourcoat enamel paints sold by White Ensign Models (a British company). Some months back White Ensign went out of business. It's been taken over by an American company, but its paints still seem to be hard to get in the U.S. And if you prefer acrylics (like me) you're just out of luck.
There's a book on Tribal-class destroyers. I haven't seen it, but on the basis of other volumes in the series I'm sure it has excellent color references. Here's a link to it: http://freetimehobbies.com/shipcraft-11-british-destroyers-softcover-book/ .
Your other alternative is one that purists will scoff at, but I happen to believe in it. Dig up all the photos and paintings of the ship you can find on the web, form an impression in your mind of what part should be painted which color, and mix up the colors by eye. And if you can't find a photo that shows exactly what you want to know - well, since nobody else can either, so what? Make an educated guess.
Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.