Problem with drip irrigation system

You have a blockage somewhere. I can't see clearly from the photos, but it appears your irrigation pipe is fed directly from the water butt via a standard hosepipe. If that is anything like my water butts, they get a lot of crud from the pipe that feeds them the rainwater, and sometimes from vent holes in the lid (I assume your lid is usually closed). That stuff - dead leaves, moss, etc - doesn't usually matter if you use only the butt tap to get water, but fine-bore irrigation pipes could easily get blocked. I suggest you fit a filter somewhere which is simple to remove and clean out occasionally, and is fine enough to prevent blockage.