I just finished quilting my first baby quilt today and washed it on the delicate cycle (as per batting instructions). The batting is a wool-cotton mix from a trusted quilt shop and it wasn't cheap.
When I took the quilt out, it had white fluff all over, almost like a layer of spider's web and I've been picking it all off.
Is this normal? And if not, what did I do wrong? Was my needle too thick so that some of the seams let batting escape?

Oh no, not sure, I'm sure others on here can help you out.

That's called bearding and is probably from the wool in the batting. Newer methods for bonding wool have made it more stable. In the past, wool battings had to be encased in cheesecloth before layering to help prevent bearding.

I prefer to use 100% cotton batting (my fav is Mountain Mist Blue Ribbon) because it gets softer with each washing, doesn't bunch up over time, and doesn't beard.

Try running a stick lint roller over it; it may help removing it.
Sorry you had that happen, I haven't used any wool bat, so no idea of the problem.

Oh ok, so it wasn't something I did wrong then. Do you know if this will continue to happen with every wash?

It is bearding, even my cotton batting is doing some bearding as I quilt.

Do you have contact paper in the UK. I use the sticky side cut off a large sheet and hand press it dowon on your quilt and just go all over it. It should come right off.

I had this happen a few years ago. I got I think it was a dollmakers needle that was, goodness, maybe 4 or 5 inches long? can't quite remember, but, I stuck it in just under the quilt top fabric and sort of swept it back and forth in between stitching areas to pull the batting back through the fabric. After that I hand washed the quilt. As long as it didn't go in the washer it was ok.

What is contact paper and what sort of shops carry it?