Hi there,
I doubt there is any way to speed this up. The order has to filter through several systems and if one goes wrong or triggers too soon then it can mess up the whole order.
There's a team that can expadite orders if there has been an issue caused by BT but for flawless orders there isn't really any process to push them.
You could try the order managment desk though.
0800 800 154 > choose order managment
Thanks
Sounds like online payments. I am using Apptivo business suite for managing my business processes including accounts, customer management. This application integrates with online payments gateways, so I can make all payments through this very easily and quickly. Try to connect them.