Two Airbus A320 aircraft, EI-DVG and EI-DER, were holding in sequence for departure from Runway (RWY) 28 at Dublin Airport (EIDW). Both aircraft had been transferred to the Air Movements Controller (AMC) on the Tower frequency. EI-DVG was stationary at the taxiway (TWY) E1 hold line. EI-DER was stationary at the corner of Link 1 and had been cleared to TWY E1. A Boeing 737, EI-EBW, was cleared by the Surface Movements Controller (SMC) on Ground frequency to taxi to TWY E1. While taxiing towards TWY E1 in accordance with its clearance, EI-EBW passed in close proximity to the front of EI-DER and stopped behind the first aircraft. No collision occurred but the margin of clearance was such that the Commander of EI-DER directly requested the taxiing aircraft to stop as it approached. As EI-DER and EI-EBW were operating on different frequencies, the transmission from EI-DER could not have been heard by the flight crew of EI-EBW. By the time EI-EBW was transferred to the AMC on Tower frequency, it had already passed EI-DER and was stopped. There was no damage to either aircraft and no injuries.