You're trying the recipe from the Independent?
Although not appearing in the ingredient list, the instructions request you to add water to the dough -- enough to get it to hold together.
Your problem is the amount of hydration -- too much or too little will give you similar results. Since you didn't mention the water, my guess is that you used too little. Gauging the approrpriate amount is a matter of "feel." Unfortunately, I can't help you too much with that, it's something you'll have to learn by experience. But as a start, whatever you did this time -- do the contra-positive next time. (Ahh, the scientific mind.)
The recipe's creator minimized the amount of water in order to keep the dumplings light, and in the belief that they would absorb enough liquid during the braise to hold together. But, alas.
Ed's egg is an excellent idea, but with a caveat. It will make your dumplings much safer, not to mention taste better; and alas will also make them considerably tougher and heavier -- no matter how gently you mix and form them.
On the other hand, if you want something very light you might try using soda water instead of plain water.
You can split the difference by substituting milk, cream, clabbered milk, butter milk, creme fraiche, sour cream, etc., for the water. This will result in a dumpling something like what we in the states call a biscuit and you don't. A "biscuit" type dumpling will also be very safe, if not quite as light as what the author intended. Nevertheless, I can confidently predict that you'll enjoy the flavor and taste.
Although, not the author's intention, it might be your best choice for its safety and also in teaching you to make American style biscuits which are a wonderful quick bread in and of themselves.
You may find this helpful: The usual ratio of flour to dairy liquid for nearly all dumplings is (very roughly) two parts flour by volume to one part liquid, or (again, very roughly) equal amounts by weight. The usual ratio of flour to water (or bubbely water) is somewhat higher. In the neighborhood of 1.5 parts flour to water by weight, or 3 parts flour to water by volume.
As a doctor -- no matter how bucolic -- you can do the conversions. I have confidence in you doctor.
Bonhomie and assurance out of the way, the reason the proportions are "very" rough is that they are contingent on a number of factors some of which can't be reliably predicted and are best resolved with "touch." No amount of careful, reproducible, scientific measurement serves as well.
If the "biscuit" idea intrigues you enough to try it, let me know and I'll write you a recipe.
Finally, I suggest searching a few dumpling recipes to get a sample which, in turn, can suggest a general idea of what's going on. The basic paramaers are: Not too dry; nor too wet; not handled too much in the mixing, kneading, and shaping; nor handled too little.