I don't know where your location is, Kath, and I don't know beans about growing a lawn. One thing I'm very
familiar with, however, is moss. It does feel sort of spongy when you step on it. If you know what moss looks like, and you think the stuff looks similar, I'd bet that's exactly what it is.
Bestlawn and the others know far more than I do. I just fight an ongoing battle with moss. It grows and spreads through the winter to the point where it threatens to overwhelm my entire house. Every spring, I have to go out and pressure wash the foundation of the house, the walks, the patio, the lower 1/4 of the fence, yada, yada, yada. Bah!