They take your money upon receipt of the application because if it went in the 'to do' pile, and then they tried taking your money 3 weeks later and there is a error with the payment, the whole thing is delayed even longer. Normally, scanning the applications and taking payment is done by someone at a lower admin level and then someone trained in the license verification process will process it at a later date knowing that all of the formalities in terms of payment are already taken care of.
Thus, if you sent it some time ago and have not seen the money leave your account I would give them a call. The e-mail inbox is very low priority and quite often takes 4-6 weeks for a reply because they deem that all info is on the website or otherwise you'd give them a call. The phone system is a nightmare and designed to make you give up and/or check the website, but if you hold on then you will get through to someone!
I'm basing this on my knowledge from a few months ago before the official EASA transition so I might not be 100% correct, but I believe that procedures would still be roughly the same.