Officers from North West Motorway Police had received reports about the grey Peugeot Partner and stopped the vehicle on the A49 Newton Road, close to Winwick.
The driver had three children in the car, aged five, seven and eight and officers carried out a drug test on the motorist.
Following the test, police arrested the driver on suspicion of drunk driving while under the influence of cocaine and cannabis.
An officer from North West Motorway Police said on Twitter that the three children had been "taken off the network" by a police patrol a relative of the children had been contacted.
Police also seized the Peugeot.