A320 Captain reported a loss of #1 Engine oil quantity and pressure. The flight crew performed and in flight shut down of the #1 Engine and continued to the destination airport.

Narrative

Aircraft X. In cruise FL370 ENG page came up. Crew noticed that the oil quantity was rapidly decreasing for the #1 engine. First suspected the problem to be a sensor error. After time; the oil pressure on #1 engine began to decrease. Crew brought the thrust lever to idle. Oil pressure decreased more. Crew attempted to ascertain it this was also sensor related and brought thrust lever to climb; but there was no noticeable increase in oil pressure. Therefore brought thrust to idle again. After some time; an ECAM appeared which directed engine master off. Crew performed ECAM actions and then ECAM for engine shutdown as well as com procedures. Crew began a slow decent; performed a single engine ILS and landed uneventfully. There were several airplanes behind us which lacked holding fuel; so crew taxied clear of runway; stopped; called FA stations; and had fire/rescue look for immediate threats. None found; FAs directed to remain seated; #2 engine was shut down and aircraft towed to the gate and deplaned normally. M/C (Maintenance Crew) was contacted by telephone and discussions regarding aircraft status and engine parameters during the event were discussed.