I seriously doubt, with the advance of aerial power happened in the twenty years between the two wars, that a war of attrition would have happened in the given scenario. More like the Stukas (at the time a more than adequate tool for infantry support. Way better than any other form of artillery) would have had A LOT to say on how the supposed battle was to end... and not well for the UK... but rather quickly, I believe. So quickly that a real war of attrition scenario would not have had a concrete way to realize itself.
I didn't say it would have been a two way war of attrition. We (the allies) would have been, bombed, panzered and overrun by the end of 1940 at the latest. We'd have lost. Comprehensively.
In your interpretation you speak of mere months before the Allies' defeat, but by its own definition "Attrition" happens if both sides can hold their own for a while... in terms of war, one year or more, before one of the sides would wear out so badly to cave in. What you described is better defined as a "rout", not real "Attrition".
Not the kind of trench warfare attrition happened during WWI a little everywhere in Europe, nor even the stalemate of the Axis against the Russians on the river Don during WWII, surely. THAT was war of attrition, what you describe... just isn't.
