Yes, you can often do this substitution and I've done it successfully many times when I've run out of milk unexpectedly, but you should know that the substitution is never going to be perfect.
On a purely mathematical basis, let's say your heavy cream is 36% M.F. You need partially-skimmed 2% milk for your recipe. If you go purely by weight (which is almost 1:1 for volume when talking about mostly water), then 250 mL of 2% milk will contain about 5 g of milk fat. To get that from 36% cream, you only need about 14 mL, or approximately 3 teaspoons of cream. (Note - don't do this, read on!)
Of course, diluting cream at a ratio of 15:1 is ridiculous and you'll end up with something that's just really watery, and that's because milk is more than just water and fat. I only provide the above calculation for illustrative purposes, to show why there's no hard rule or even rule of thumb for this particular substitution.
With normal cream, most people go with half water, half cream, or if they're trying to approximate skim milk then maybe 1 part cream to 2 parts water. If you have double cream, I would probably use 1 part cream to 3 or 4 parts water; that will give you a reasonable approximation of the consistency of whole or skim milk without making it too watery.
Please keep in mind that different recipes/preparations use milk for different reasons, so this isn't going to work everywhere. I certainly wouldn't do it in baking, but for many stovetop recipes, the main purpose of the milk is just moisture, so you're fine to substitute cream + water and it doesn't really matter if you're "exact" - which you can't be anyway.
Quite simply, it's the fat content.
Whole milk or "full-fat" milk is 3.25% fat by weight. Heavy cream is 36-40% fat by weight. These two products are at opposite ends of the fat spectrum, and there's very little difference between 1% and 3% when it comes to an item such as caramel sauce, for which the optimal ratio is about 50% fat. (A little butter can boost the fat content from 40% to 50%).
You might be able to substitute standard/single cream (18-20%) or maybe even coffee cream/half-and-half (10%), but any lower than that and you're just making sugary milk.
Other alternatives to (possibly) get it thicker:
Use (much) less milk; I'd advise not attempting a direct substitution, just find a recipe based on milk. Even the best milk-based caramel sauce will still be substantially runnier and/or grittier than a cream-based sauce.
Considering that butter is 80% fat and homo milk is 3.25%, you could use a mixture of (approximately) half milk and half butter that would emulate the fat content of heavy cream. I've never tried this personally, and I suspect that the flavour might be a little off, but at least it would be closer to the expected texture.
Try a reduction (simmer off the water in the milk). You'll be simmering a long time, and you'll have to watch it very carefully to make sure it doesn't burn, and you'll probably have a nasty stuck-on mess to clean up in the pan afterward, but it will thicken.
Best Answer
The difference between whole milk (or any milk, really) and half-and-half is one of fat content, not overall concentration. Half-and-half gets its name from being a 50/50 blend of milk and cream, which normally separate because the less dense fats concentrated in cream float naturally to the top of the mostly-water milk. However, milk also contains a number of other proteins, sugars, etc. that give it flavor. When you dilute half-and-half with plain water, you're diluting the fat content (potentially down to a similar range as contained in whole milk) but you're also diluting all those other flavorful components. You wind up with something that has the right fat level but not enough of anything else, and which tastes somewhat flat and flabby by comparison with proper milk.