That looks pretty fungusy to me.
First, 100% peat is not what I would suggest for U. longifolia. I am not sure if it is actually classified as epiphytic or not but I grow mine in some ways at though it were. I have mine in a hydroponic mesh pot. It has been a while since I divided it but as I recall I am using a mix of LFS and perlite. I can check for sure when I get home.
I let it sit in a little bit of water sometimes but have found that it seems to do best being top watered fairly frequently rather than sitting in standing water all of the time. In fact, I noticed a U. longifolia I dontated to a public collection died recently. Where was it? Sitting flooded in standing water.
I think Tony Paroubek's suggestion of pulling out a plug and repotting it is a good idea- and in fact probably your best shot at recovery. Naturally, try to grab one with as little fungus as possible. I would try to get as much of the soil off as possible by aggitating it under some water. This will naturally stress the plant (which is already stressed by the fungus). So I would try to get a few plugs just to be safe. I would also try to get a plug or two with very clean looking soil and plant without agitation just to be safe.
I do not know if these work for U. longifolia or not, so proceed with caution. Some anti-fungals which seem to work in other contexts would be some sulpher spray (I buy the dried powder and add to water but you can find pre-mixed sulpher spray in garden centers- just make sure there is nothing nasty in there like copper). That might be worth trying. Another remedy that might be worth a shot is 9 parts water, 1 part milk sprayed on the afflicted area. Again, I have not tried these but they are known to work- at least as a preventative in other plants. I suspect the milk trick might cause problems though given the high mineral concentration in the milk.
Last thought- give them lots of good light. The more energy they have, the better their defense system.
"Hey there, I find that some watered down chamomile tea helps to get rid of fungus/mold problems with my utricularia"
Never heard of that! I will have to try that out. Thanks for the suggestion!