P0401 exhaust gas recirculation flow insuficient detected

Really, code P0401 means Insufficient EGR Flow
EGR stands for Exhaust Gas Recirculation. It is part of the vehicle emmissions system, and is used to reduce combustion temperature and pressure to control Oxides of Nitrogen. There are generally three parts to the EGR system: the EGR valve, an actuator solenoid, and a differential pressure sensor EGR (DPFE). These things work together to deliver the correct amount of recirculation based on engine temperature, load, etc. The P0401 code means that OBD detected an insufficient amount of EGR.

Symptoms: You may notice drivability problems such as pinging (a.k.a. pre-ignition knock) when the engine is under load or the vehicle is at higher speeds. There may also be other symptoms.

Causes: A code P0401 most likely means one or more of the following has happened:
The DPFE (differential pressure feedback EGR) sensor is faulty and needs to be replaced
There is a blockage in the EGR (tube), most likely carbon buildup
The EGR valve is faulty
The EGR valve may not be opening due to a lack of vaccuum

Keep in mind this possible solutions, in fixing this code, it is quite common for people to just replace the EGR valve only to have the OBD code return. The EGR valve is not always the culprit.
Use a vacuum pump and pull the EGR valve open while monitoring engine RPM's & DPFE voltage. There should be a noticable difference in RPM's with the EGR open
Clean out the EGR valve and/or tubing to remove deposits
Check the voltage at the DPFE, compare to specified values (refer to a repair manual for your specific model)
Replace the DPFE sensor (with a good quality / OEM one)
Replace the EGR valve


Test, check it and keep us updated.

Depending on the year make and model of the vehicle, the most likely cause of this code is the DPFE sensor which controls EGR operation.