There answer is yes and no.

It depends which service you are using.

FTTC (Fibre to Cabinet):

With FTTC the Cabinet is the green cabinets we see on our streets, this means that the fibre cable runs from the exchange to the cabinet.

After the cabinet is copper wire and with this setup you can utilise an older modem/router.  However, Fibre to the Premises (FTTP) is different.

FTTP (Fibre to the Premises):

Fibre to the Premises means that the copper wire from the cabinet to the premises (your home or business) as the old routers are not fibre enabled, you will have to get a router that fibre optic connectors can connect too.