Yes, it's fungal. The spots don't have a distinctive "halo" so that rules out Early Blight. The first of the two photos I posted above shows Septoria Leaf Spot. Your spots look too big. The water-soaked look around the spots and the yellowing on the other side of the leaf suggests good old Leaf Mould to me.
Here's what it typically looks like, top of leaf and bottom:
Look familiar? There was a thread largely about it only the other day. It's about the most common fungal problem with greenhouse toms, in fact it's rarely if ever seen outdoors. Unfortunately, like all fungal problems, there's no treatment once it's established. All you can do is remove and destroy affected foliage. And wash your hands before touching healthy foliage.
Unless you spray preventively, your only defence against these problems in a greenhouse is as much ventilation as possible - a friend of mine used an electric fan on low speed to aid the air circulation - and keeping the foliage as dry as possible. But, as I say, it's very very very common.
One of the unfortunate ironies is that there's a school of thought that the PL varieties are less susceptible to fungal problems. Never believed it, myself.
The ultimate danger, obviously, is defoliating the plant. I'd even take the plant out of the greenhouse for a while if that's at all possible.