I find peat free compost absolutely crap. I now use Irish peat for most things.
I went to a nursery for something some years ago now and noticed they were potting up plants in a medium that was not on sale outside. Got chatting with the owner about compost and how disappointing the run of the mill compost was, he said we can't grow in that stuff. He sold me half a dozen bags of what they use and it's Peat with additives. I mix with a bit of sharp sand and sieve it.
I don't know what it's like for Late Blight where you but it's hard to grow out door Tomato's because of it here.
T