An Air Carrier pilot reported while taxiing they had to abruptly brake to avoid a collision with a van driving across the taxiway causing injuries to the Flight Attendants.

Narrative

Company pushed back from Gate ZXX for single-engine taxi westbound on Taxiway D for takeoff on Runway XX. Disconnected from the tug and set parking brake on Taxiway D; heading southwesterly; I.E.; angled 45 degrees from the terminal and parallel taxiway. Weighing approximately 165;000 lbs. I advanced power to 45% N1 on engine #2 (right engine) and slowly built-up momentum to first move forward then turn back to the right on the D Taxiway heading westbound. I estimate we were entirely re-centered on Taxiway D abeam the midpoint between gates ZXY and ZXZA lead-in lines. For clarity; east to west; the gates are: ZXX-ZXY and ZXZA/ZXZ and ZA-ZB. The next several events occurred in very rapid succession. As we approached Gate ZA the First Officer called out a white van fast approaching us; on our right nose; headed south on the painted ground vehicle lanes. The north end of the ground vehicle lane is near the lead-in line for Gate ZC and the south end is approximately halfway between the lead-in lines for Gates ZA and ZB.I immediately reduced the power to the idle stop and simultaneously began braking. As the vehicle appeared to accelerate; I quickly determined an immediate stop was required to prevent an imminent collision and depressed the brake pedals to the maximum. As previously briefed; the First Officer also applied the brake pedals. The white van continued and did not stop. I estimate we were only moving approximately 15 kts. and we stopped quickly. The abrupt stop caused three Flight Attendants performing their duties in the aisle to lose their balance and all three were thrown to the floor. One Flight Attendant was unable to get up of her own volition and I was concerned she might have a serious spinal injury. The other two Flight Attendants had apparently sustained less serious injury and were able to regain their faculties. I set the parking brake and using the PA; stated ' Flight Attendants; check in'. Purser answered immediately and gave me an initial report that all three Flight Attendants had been knocked down and two had gotten up. Ramp witnessed the event; asked us if we had any identification markings from the van and immediately dispatched an airfield ops representative to track down the driver of the white van. We contacted Company Operations and asked for medical assistance to be dispatched to us. Operations wanted us to taxi to a gate. I declined that suggestion as we had no idea how seriously injured especially the one Flight Attendant unable to get back up was. The First Officer and I discussed next steps and based on the lack of clear response from Company Operations we asked Ramp to request medical assistance. We sent an ACARS message to ZZZZZ and gave an initial report and expect return to the blocks. An off-duty Flight Attendant; still in uniform; commuting to ZZZ1 volunteered her assistance and I accepted it. That information was given by phone call to ZZZZZ; in effect recruiting her to our crew for the later taxi to the gate. We made several announcements to passengers throughout. The ARFF responded with a ladder truck; and ambulance; and one or two other support vehicles. We shut down the engine; switched to APU power and air conditioning; the landing gear was chocked by ARFF; then at my direction we disarmed and opened door 1L while leaving the other three doors in an armed condition. EMTs entered the aircraft via the ladder truck; evaluating the three Flight Attendants first. The Flight Attendant who was unable to get up was taken to a waiting ambulance in a Stokes-type litter with a cervical collar supporting her neck via door 1L onto the ladder on the ladder truck and then lowered to the ground; then loaded into the ambulance. The EMTs evaluation was the other two Flight Attendant injuries did not require immediate removal and could perform their duties for a short taxi to a nearby gate. The Flight Attendants agreed they could perform their duties to the gate; two EMTs were specifically assigned; one to each Flight Attendant for continued evaluation.It is my understanding the EMTs surveyed all the passengers for injuries. No injuries were reported to me. Once all other ARFF personnel had vacated the aircraft; we closed door 1L; re-armed it; and started both engines for the taxi into the gate. Once the ARFF vehicles were clear; station operations assigned us Gate ZC; a couple hundred yards and left turn into the gate. We parked and performed normal parking procedures. We wrote a precautionary hard braking write-up for Maintenance. They performed an appropriate inspection and signed off the Maintenance write-up; sending a new Maintenance Release Document. We were met at the gate by representatives from all appropriate departments; especially Inflight Services who had replacement reserves to immediately swap with our injured Flight Attendants. Customer Service was available to make announcements to our passengers to supplement my announcements. The First Officer and I conversed with each other; doing an informal self-evaluation (IMSAFE) and felt we were fit for continued duty. We contacted ZZZZZ; requested a fuel top-off and new release. We contacted the Chief Pilot and conferred with him. He agreed we could continue with the flight ZZZ to ZZZ1. Inflight Services re-crewed four new Flight Attendants; and we had a routine flight to ZZZ1. Upon deplaning it is my understanding a passenger claimed to have been injured with the abrupt stop in ZZZ. This passenger was referred to the gate agent in ZZZ1. I had only post-knowledge of the claim as the passenger had already departed the aircraft without assistance.