It does make a difference. The evidence has gone up in flames.
Prepare for an "inconclusive" on cause of death, then. Or maybe a "ooh, we've lost the samples we took, wot a shame" (what a surprise). It can all be brushed under the carpet now the corpse has been incinerated and there's no scope for further tests. We won't see a "she was pissed as a newt and drugged up to her eyeballs" or anything like that, I bet.
The corpse should have stayed on ice locked away until the inquest has been concluded. Then the evidence is still at hand and truth can't be suppressed so easily.