Quite easy to distinguish. Buy your bats from a reputable bat maker direct, or a reputable retailer who will guarantee that if you want a bat made from UK grown English Willow, then that is what you'll get 😁
Generally speaking I'd agree, although Kookaburra and GN both had junior (and a handful of senior) bats made from what they called 'alternative willow' and 'European willow' a few years ago. The definition in the catalogues was pretty ambiguous and not as clear cut as the difference between English and Kashmir willow for example. For a retailer who perhaps offers multiple sports and doesn't really check (but is still more than reputable) it would have been an easy mistake to have sold these bats as English willow and a customer would be none the wiser.
I think Kook and GN (and anyone else who was at it) have tightened up on this and made things clearer now.
The issues will lie with brands who get bats made (especially if made overseas) by a third party. I am purely using them as an example and not making any accusations or suggestions at all, but lets say SG decide they are going to buy in a load of Serbian willow and replace the lower end of the English willow range without telling anyone, Kookaburra will end up with a load of Serbian bats that they don't know are Serbian.
Knowing how certain parts of the industry work, this isn't beyond the realms of possibility at all. So yes, you could walk into a reputable retailer, ask for a bat from a reputable brand, the retailer and the catalogue both say it is English willow, the brand has sold it at an English willow price to the retailer, and purchased it themselves at an English willow price from the manufacturer. Only the manufacturer knows what it is.