I ordered a broadband service on Saturday, and since Sunday I've had the message:

Your order details are currently in the process of being sent to BT by our automated system. This process can take up to 2 hours to complete. 

...so a bit more than two hours!

 Is this pretty standard or should I be calling customer service? 

Probably worth checking.
I would have expected it to be submitted by now and the order acknowledged by BT.
Usually this happens automatically fairly quickly, but there can be exceptions...

Send an e-mail to customerservices@zen.co.uk or give them a ring to check on it if the status hasn't changed by tomorrow morning.