For ADSL most reputable ISPs require their username and password to be
configured in the router. In general it does not matter where the phone
line is, so long as it is provisioned with ADSL.
The exception is BT and maybe some other ISPs whose customer base is not
considered able to configure a router. In this case a non-ISP supplied
router may require a username and password in order to complete its
configuration but the actual values are irrelevant; the authentication
is by virtue of the phone line.
For FTTC most ISPs will provide you with an appropriate router with
integrated modem, for the cost of postage. In the past the ISP could
ask Openreach to provide a modem as part of the service that the ISP
bought from Openreach, but I think the facility was dicontinued in
February 2016. Such a modem does not have any facility to be configured
with the username and password; it simply presents an Ethernet
connection to the router, and the router is configured with the username
If you want to configure your own router and modem, that is indeed
possible. For example the Vigor 130 ADSL/VDSL Modem
.... will allow router with an Ethernet WAN port to connect to either
VDSL or ADSL. Certain Vigor routers can view the line parameters
(speed, SNR margin, error rate) from the V130.
In general, routers are not 'plug and play' you would expect to
configure them with a username and password.
Some ISPs will pre-configure the router they supply with the correct
credentials. Others will configure the router they supply to use the
TR-069 protocol for remote configuration of the router - see: https://en.wikipedia.org/wiki/TR-069
There is nothing to stop the user from disabling this facility on a router.
Hope this helps.