There are 7 categories of yarn, I've listed them below with their closest UK type and also the hook size that is usually used with the yarn category.
To add to the confusion the hook size and the knitting needle size are often different for a yarn ... and usually the yarn band only states the knitting needle size (what is this crocheter discrimination ???!!!)
I have tried to put all the information that you would need to "calculate" the correct yarn in the table below.
Here is a handy PDF file containing all of these conversions and more Conversions
I've included the wraps per inch (WPI) measurement, you can use this where you don't have the yarn band anymore or if you are recycling old jumpers etc.
To measure the WPI you need a pencil or pen and a ruler or measuring tape. I find it easier if you cut a nick into the top of the pencil to hold the yarn tight, then just wrap the yarn around the pencil until you have covered 1 inch - using your ruler or measuring tape to measure.
When you have covered exactly 1 inch count the wraps (in the image below 13) and that is your WPI. You may find that the WPI doesn't match a yarn type exactly but you will get a reasonable understanding of the yarn type you have.
Then comes the question of hook sizes, clearly it would be too simple to have a standard :)
There are metric, US and old UK sizes. Rather confusingly there is a cross over between the steel (or thread) hooks and the plastic hooks in sizes. I've split them out to (hopefully) aid clarity.
Here are the conversions;
Another link to that conversions file.