Even if Curve didn’t block it, you’ll often find that the National Lottery itself blocks Curve. Soon after I first got my Curve card in 2016, I tried to use it on the National Lottery web site and it was rejected. When I asked the National Lottery why, they told me that it was because the card was prepaid and commercial, and that prepaid cards are available to under-16s, whereas one needs to be 16 or older to play. However, this argument didn’t hold water, given that non-prepaid debit cards are likewise available to under-16s.
My current Curve card, which is still commercial with a BIN of 5375 91, is immediately rejected by the National Lottery web site when I enter the number, before I even get to the authorisation stage.
The National Lottery refuses to accept credit cards because it doesn’t want players getting into debt in order to play. I therefore questioned why they likewise don’t accept American Express charge cards (which must be paid in full with no option to defer payment and pay interest), and they couldn’t explain that. Therefore I am sure that, if the National Lottery realised that Curve allowed funding to an underlying credit card, it would be a further reason for the National Lottery not to accept it.