Hello @lovetoprint, I had a flash of inspiration last night and have sorted out the problem for me.
Go to the actual subscription form and into edit mode. Go to the Storage option / SquareSpace Email Campaigns (make sure it's on) and then make sure you've added the correct mailing list - mine wasn't ticked previously.
I had added my automated email after creating the subscription form so hadn't gone back to update it.
I hope that helps!
Cheers, Kate