A Broadbent router is optional. At checkout you can choose to use your own.
What you still receive
The circuit is still given its addressing. On symmetrical full fibre that includes a static IPv4 address, assigned after the line is live. Other products use a dynamic address unless you ask for a static IP.
Your router has to support the access type for that circuit. The order does not include a compatibility list for third-party hardware.
On the install
A standard Openreach visit connects the router, checks one device, and runs a sync test. Have the router you intend to use available for that test, and a power socket within the distance the install allows.
If you would rather have a router configured before it arrives, order the TP-Link that matches the speed. That choice is covered in which router full fibre uses.