Actually, for "down home" commonly used desserts one would find everyday here in the U.S. the fare tends to be pretty mundane... puddings (made fro Jello mixes), ice cream, pie and cake. Seems if the lady of the house wants to embark on something different she looks for a French or Italian recipe.
However, for a truly American concoction you could try S'mores... easily done and the kids love them.
Youll have to find some Graham Crackers (I've seen them described in the U.K. as similar to your "Digestives") seen here:
http://www.amazon.com...ackages/dp/B0016510LG and some of Hershey's Milk Chocolate bars (not nuts, just plain, and some fluffy, large size marshamallows.
Take two sections of the Grahamcracker and place about 4 to 6 squares of the Hershy bar on one, followed by one large Marshmallow. Place it on a baking sheet in a 350 degree (F) oven for just a couple of minutes... enough to melt some of the chocolate... take them out and give 'em to the guests...
Or... you could spend an afternoon making a lattice crusted apple pie and homemade vanilla ice cream...