Was this stuff not already in the hands of the Leicester Police by this time? Surely UK police forces can freely share intelligence sources.
From what I've read, the report and the e-fits somehow got transmitted to both LP and the PJ in 2011. It may therefore not have involved the Met in legal wrangling to get the report / e-fits out of Oakley itself.
However, did the McCanns have a copy at the time that they could legally have used?
Some people associated with Oakley were disgruntled that they hadn't been paid, although the Fund had paid Oakley or whichever official business entity, until the Fund got suspicious and cancelled the last leg of the renewable contract. Halligen should have paid the sub-contractors, but apparently didn't and was then arrested and convicted in the Trafigura saga.
I find it entirely possible that the Fund refused to pay a second time, but were trying to get hold of a copy that they could legally obtain / use. Possible issues are that they couldn't physically obtain or couldn't have used a copy from Oakley pending the outcome of whatever litigation, and / or that they had been given a copy under judicial secrecy by either LP / PJ.
However the Met got hold of it, it was then up to them to no doubt double-check, then choose an appropriate media-friendly moment to publicise them.