A320-200 pilot reported during initial approach they had a near mid-air collision with a VFR aircraft that was flying opposite direction in the approach corridor resulting in a TCAS RA.

Narrative

This report concerns profound failures by ATC leading to a near-midair collision. On arrival to ZZZ; after being handed off to Approach we descended to 4000 feet on a southerly heading. The approach in use was ILS Runway XX. The Approach Controller was busy working quite a few aircraft. We received a call from the Approach Controller for traffic ahead; a Cessna 400 feet above you." She provided no other information. We replied that we were "looking for the traffic." At no time during this approach did we ever report any traffic in sight. At this point we had the traffic directly ahead of us on TCAS at about 10 miles; also indicating +400 feet. We looked diligently for the aircraft and finally saw it (a single-engine prop like a 152/172) as we approached 5nm separation; now slightly to the right of our course. The Cessna was apparently flying westbound; parallel to and in the opposite direction of the ILS Runway XX final approach course that was just a few miles to the south. We were discussing our options and wondering what approach was planning when the controller (a different voice) gave us a turn to the west. We made that turn and began to pull ahead of the Cessna. Eventually it disappeared from the TCAS display as it fell behind. During this time the Approach Controller was busy giving vectors to other aircraft and taking new hand-offs from Center. He never mentioned the Cessna traffic.The Approach Controller then gave us a turn back to the south towards the final approach course. As we rolled out of the turn we got an immediate RA "DESCEND DESCEND". There was no traffic advisory prior to the RA. As pilot flying I complied with the RA until the TCAS system stated clear of conflict; then leveled off. We never saw the Cessna.Once we were stabilized we called Approach and told them that we had responded to an RA. The controller acknowledged with an "OK" then went back to vectoring other aircraft. We had to assertively inquire what altitude he wanted us at now and what heading we should take since we were about to cross the final approach course. He turned us toward the airport and we completed an uneventful approach and landing. He never mentioned the Cessna. After parking at the gate I called the Approach Control facility and spoke with a supervisor. He seemed unaware of the situation. After giving him a brief summary of what happened the only thing he asked is whether we had called the traffic in sight at any time. Again; we had not.This event has many disturbing similarities to the recent mid-air collision in DCA. Approach Control was tolerating a VFR general aviation aircraft flying very close to a very busy instrument approach corridor. It was not clear to us whether approach was even communicating with the Cessna. The Approach Controllers made a single call to us about traffic; seemingly unconcerned about an aircraft directly ahead of us and only 400 feet above. After the first call there was never any communication from ATC about the Cessna; even when they turned us directly into its path. This situation reeks of complacency by the local Approach Controllers; who may be accustomed to seeing VFR aircraft traveling close to the final approach path to the airport. Furthermore; it was extremely lucky that the Cessna was reporting its altitude (obviously not always the case for small civilian aircraft). With that information our TCAS was able to give us the "correct" instruction to descend. Without that is possible that we might have climbed instead directly into the conflicting traffic. Again; ATC was of no assistance. Finally; it seems likely that there was some kind of conflict alert that was ignored by the Approach Controllers; since both aircraft were reporting position and altitude. Again; controller complacency and misplaced priorities seem likely factors.In hindsight I should have been more proactive about asking ATC exactly where the Cessna was before I executed the final turn to the south. I mistakenly relied on Approach Control to provide separation between two aircraft that were both reporting an accurate position and altitude.Cause: Controller complacency and perhaps normalization of deviance.The FAA should institute much clearer directives for Approach Controllers to further separate IFR and VFR traffic in the vicinity of major airports; as well as to prioritize immediate responses to any alerts about conflicting traffic."