Replacing BT Modem with a Draytek 2866 in a Bright Box 1 setup

[Agent-J]

I am currently using an EE Brightbox 1 via a BT modem in bridged mode to allow access to the internet. 

I'd like to replace the BT box with the Draytek, as I would like to have an additional wired network, via the Draytek, that would be operational, and connected to the internet, even when the EE box, that i'll use just for Wifi, is switched off. The Draytek is a modem and a router. 

I'd ideally like the networks to be connected somehow so, for example, wireless printers connected via the bright box could be accessed from the wired, Draytek connected, network. 

Is there an elegant way of configuring the Draytek to allow for this so I just have the to boxes, or do I need to still use the BT modem and connect both the Brightbox and the Draytek via an additional switch to enable the setup I need?

If anyone could help it'd be appreciated. 

[XRaySpeX]

@Mustrum : Probably due to my unfamiliarity with modem-onlys. I misconstrued the OP into thinking that the Draytek was principally a modem with an integrated router built-in that could somehow service 2 routers, its own & an external 1, the BB1, in parallel, not in series as is usual often leading to a double NAT.

On thinking further on it I realised that while this may work for outgoing access, any incoming access would have to 1st hit 1 the Draytek's router before it could be decided if it needed to be passed to the other router. Therefore requiring them to be working in series.

This together with your comments finally led me to realise that the Draytek is a conventional modem router that could be configured (by default probably) to operate in bridge mode as a modem only, unlike all of EE's routers. But the OP doesn't want it to operate that way (just like his original OR modem).

You, quite rightly, pointed him at using the Draytek as the main modem Ethernet router & the BB1 as a WAP, based on my "2nd Brightbox as a WAP" article.