OK so this world I'm building has Earth-like flora and fauna, along with being around the size of Earth and being around the same distance as Earth from a star the size of the sun. The atmosphere is similar to Earth's as well, and the climate of the land area of the planet is temperate oceanic, similar to that of Britain or Ireland. Would it be possible that in the forests of this planet, trees are joined by tree-sized mushrooms? (When I say tree-sized mushrooms, I'm thinking ones around the size of huge red mushrooms from Minecraft, so not super tall but large enough to provide some fungal lumber)
Now, the first trees evolved on Earth right around the same time that Prototaxites went extinct, so perhaps trees just out-compete them and they really can't co-exist... but it's not entirely obvious why Prototaxites disappeared when trees showed up. If they were actually lichens, relying on photosynthesis from their algal component to survive, then it makes sense that they would've been competing for light, but otherwise there's not a whole lot for a mushroom and a tree to compete for, and they should be able to co-exist just fine.
So, just make your giant mushrooms actual mushrooms, and not lichens. If they don't photosynthesize, or don't rely on photosynthesis, you will need some other excuse for them to grow tall, but that's easy to manage--maybe they do it for seed dispersal, for example.
My comment as an addition to Logan R. Kearsley was too complex, but see this as an addition to his answer.
It would make it more difficult for a mushroom to grow into a treelike structure than a lichen. They draw energy most often from either living things or the decaying matter. That means it requires a constant source of other living things to grow, while not competing with too many other living things for space.
That being said: meet the Humongous Fungus. https://www.google.com/amp/s/www.businessinsider.com/largest-living-organism-the-armillaria-ostoyae-fungus-2017-5%3famp I just grabbed the first google link, but should tell enough of the basics. It can grow huge and has here and there small mushrooms that break the surface (which incidentally is also how mushroom rings form. Certain kinds of fungi growing underground mostly circularly and grows our well known mushroons at the edges to spread it's seeds).
You can take lessons from it and have some fungi grow large underground, breaking the surface here and there to grow large treelike fungi. To add to this, fungi can do more than just decay things. They are used everywhere for communication between plants in exchange for nourishment. http://www.bbc.com/earth/story/20141111-plants-have-a-hidden-internet (again, first google hit. I didn't really read it but should tell you the general stuff). You can use this for a less destructive form of the fungi.
So with some changes that are unlikely but not unrealistic, yes it might be possible.