Medium Large Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Workload; Situational Awareness
ATC Issue All Types; Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Overcame Equipment Problem; Flight Crew Returned To Clearance
Aircraft; Human Factors; Procedure
While on approach into EWR ILS4R we were on a vector of 090 degrees and leaving 4000 for 3000 feet - our assigned altitude. As we were leveling off; ATC asked for an immediate speed reduction from 250KIAS to 200 KIAS then descend to 2000. As I spun the Airspeed back to 200 the aircraft leveled at 3000 in ALT HOLD which is what we needed to slow the plane and speed brakes were extended; then flaps as we were nearing the localizer for 4R - still not cleared for the approach. We were vectored across the LOC given a 030 heading to intercept and reminded to intercept. 'Heading 030 intercept LOCALIZER and descend 2000 now maintain 2000 till established then cleared ILS 04R'. To add to our workload; my ILS had an identification; but the first officer's ILS receiver was not showing the identification. It was then we realized we had failed to descended to 2000 feet after slowing as we had expected to intercept; not be vectored across the localizer without warning; while configuration changes and speed changes were being made. It was a high workload time with several non-standard ATC instructions. (Including descending below a published ILS step down altitude). We immediately descended to 2000ft. Intercepted the LOC and completed the ILS 4R without further issues to a successful landing. Our high workload as we configured for approach and landing caused us to inadvertently omit the last step of our descent instruction.
Captain reported receiving a last minute vectoring through the localizer; after they had overlooked  descend to an assigned altitude which happened to be below a step down altitude for the ILS 4R into EWR.