I got some more advice on Usenet (soc.motss, of all places). It seems that the "oatmeal" called for is actually more like what Americans call oat *flour*, or at any rate contains a fair proportion of fine particles. Oat flour is widely available in the U.S., and I found it at my local supermarket. I tried it this morning, with sure-enough lumpy and quite edible results. It was not clear what the right ratio of milk to flour should be, but I tried 3:1, which is what I use for Quaker Oats (with water & a little milk). The result is a bit thick. I expect I'll try more milk, and mixing some coarse meal in with the flour.

I see from the OED that "treacle" usually means molasses but may also include maple syrup, so my New England treatment is not technically wrong, tho I don't suppose one sees much maple syrup in Staffordshire.