A BAe-125 returned to their departure airport following the failure of the pressurization system shortly after takeoff.

Narrative

We departed Runway 35 with me occupying the right seat as the non-flying pilot and with the APU on. Tower cleared us on runway heading to 2;000 FT. After establishing a positive rate of climb we retracted the gear and I opened both main air valves and at 600 FT AGL I shut down the APU in accordance with the SOPs. Shortly afterwards I noticed that the cabin rate of climb was still around 2;000 FPM; exactly the same as the rate of climb of the aircraft. I stated to the flying pilot that I believed we had a pressurization issue and would need to trouble shoot. We complied with Houston Departure instruction to level at 3;000 FT noting that the cabin climb rate continued to correlate with the aircraft rate of climb.At this point I verified the position of all associated switches and systems and no abnormalities were noted. Both of us agreed that we should make a final assessment of our pressurization condition during the next climb segment. ATC cleared us to 16;000 FT and immediately after starting a climb we observed the same excessive cabin rate of climb and no cabin pressurization. We concluded we could not conduct the flight with the aircraft in this condition. I contacted ATC who cleared us to level at 6;000 FT with which we complied. We did not declare an emergency. I further notified ATC we intended to return to ZZZ; but we needed to burn off some fuel first. ATC issued delay vectors. Flight conditions were VMC.After verifying that we were now below max landing weight we ran all appropriate checklists; notified ATC and were vectored for the and ILS approach and an uneventful landing. After several checks on the ground we determined that most likely the automatic pressurization controller had failed.