There are two types of Dunlop (or English) valves. I shall come back to these below. All valves have commonalities.
First of all, one has to overcome the pressure in the tire before air flows into it. Unlike the valves on a car, the valves on bicycles are check valves that are held close by a higher pressure on the inside. When you pump, you will sense that the pressure builds up in the pump, its hose, etc, until suddenly the valve opens and the air streaming in may be heard.
Any valve may also have dirt or other objects in side, check if your valves are clean. You can remove Dunlop valves and wash them in water with a small amount of dish-washing soap.
The higher pressure in the tire pushes as rubber hose against a hole in the valves stem, sealing it. This type of valve is now uncommon in most of Europe, but may still be found on older bikes or, for instance, in China.
The rubber hose may degrade. This typically leads to the tire leaking. That it sticks to the hole is conceivable. Tire repair kits often have these little hoses included. In a pinch they allow for quite a lot of improvisation. Otherwise they ought to be replaced with the new type.
It is conceivable that the rubber hose is very tight and that you have to blow it up like a balloon first. However, that is just a wild guess. I have thrown these valves right away when I found one in an old bike.
A small rubber or metal ball inside a ferrule is pushed by the internal pressure up against the valves opening. A very common type of valve in parts of Europe. This type of valve is often called a Blitzventil in German speaking countries.
This valve is somewhat susceptible to dirt, and ought to be used with its cap only. Usually dirt will prevent proper seal such that the valve leaks a little. Oil, grease, or harsh detergents may foul valves with a small rubber ball. It is conceivable that it gets sticky and clings to the opening.
Some of these valves tend to become slightly harder to open when they were pumped to a high pressure before. In that case the rubber ball is wedge very hard against the valves opening, and it takes more force to push it inside. Since one has also to work against the pressure in the inner tube, it may be significantly harder to pump it up.
In my experience, this is not much of an obstacle it just takes one tough pump stroke, and its free. However, your valves might be worse in that regard. If cleaning doesn't help, consider replacing the valves with other Dunlop valves. They cost about 0.5 Euro a piece.