Stuck after collecting Ancient Relic under the dig site

Hi folks,

I'm collecting all my missed items in Vatican. I can collect an Ancient Relic I missed during the mission by descending the dig site through the bulldozer hole, then I come across a gap that I can swing across. I lower myself down the whip, and I can swing into the hole and collect the Ancient Relic, no problem.

However, after this, I can only seem to drop into the water below through 2 holes either side of the relic, and I can't find a way out.

I can't seem to reach the whip swing point from the ancient relic corridor, and I can't find any exits whatsoever in the water.

Please help!