>Definitely a pudding rather than a dessert<
Well, Stateside, a pudding, (aside from plum pudding, which is always from a tin) is a soft custard like food, almost always a dessert. Very similar to "bird's custard", only its usually served cold, rarely warm, and never as a sauce!
Cooked milk, sweetened and flavored, and thickened with corn starch (most common) or arrowroot and then cooled before serving-- and frequently topped with ersatz whipped cream.

Am I right in thinking Toad in the Hole is an egg fried (poached?) in a cut out circle of bread? But Frog Spawn? I have never even heard of that!