Cessna 172 pilot reported encountering wake turbulence on approach to BFI in trail of a preceding jet aircraft.

Narrative

Headed into BFI on VFR arrival from the west from ZZZ planning for the Blake Island VFR arrival. Called Tower with current ATIS; and requested the Blake Arrival. Tower was busy with other traffic and instructed us to hold over the island and that Tower will call our inbound leg. We held for about 3-5 minutes; monitoring the frequency and scanning for traffic. After which Tower told us we can continue inbound on the Blake arrival and report 3 miles from field. Which we reported as we got closer. Tower then cleared us to make right base on 14L and cleared to land number 1 (crossing the centerline of the parallel 14R runway). At the same time another Cessna in the pattern for 14L proceeded to turn left base for 14L. I had sight of them at all times but became concerned as soon as they turn downwind to left base. As we continued to converge head on I quickly radioed Tower asking if we should perform a right 360 for spacing; but in the frenzy I forgot to say my tail number; which led the Tower to believe that the opposite traffic made the radio call. Tower then said yes to make the right 360 and asked if that was for the other Cessna and not us; I quickly piped up and told Tower the tail number of our plane and if we should make a right 360. Tower told us negative for right 360 and that we were cleared to land 14L. Tower then called up the traffic and told them to pass behind us and to maintain visual contact. While Tower was calling them up I quickly angled my nose to the runway to get in front of the traffic as they were on final. Narrowly passing in front of them that was too close for my comfort. However; this was not the end of the problems as Tower never advised us of a previous jet that had landed some minutes before our approach on the parallel runway. As we were about 150 ft. AGL we suddenly hit wake turbulence and entered into an uncommanded extreme left roll. I quickly added full power; being prepared to go around and full opposite roll to stop the effect. We then proceeded to land without any further incidents.It is of my opinion that the error started as a result of Tower clearing us too soon for the arrival; and that if Tower cleared us when they did; to let us go behind the left base traffic. However as Tower was extremely busy managing other traffic; the Controller could have been flustered because of it.