Crumbles originated in Britain during the 2nd World War. As there was strict rationing the ingredients needed to create the bases of a normal pie weren’t available. Pie’s would require too much flour, sugar and fat to make the pastry. So people in the 2nd World War got creative and made a simple mixture of flour, margarine and sugar and used this to make the top of the crumble. The dish is also popular due to its simplicity.
And FYI - Some parts of America also have crumble however they call it CRISP.
There’s nothing quite like apple crumble with a healthly dollop of custard