Hi limbo,
I have the BT supplied modem & a Netgear WNR1000 router as supplied by Plusnet for an ethernet connection from the BT modem.
The modem as supplied by BT cannot be monitored as it is locked, but the Netgear router maintains an activity log, showing stuff like this:-
[Time synchronized with NTP server] Tuesday, Aug 30,2011 18:56:38
[Internet connected] IP address: 91.125.94.116, Tuesday, Aug 30,2011 18:57:00
[Internet disconnected] Tuesday, Aug 30,2011 18:48:53
[Admin login] from source 192.168.1.100, Tuesday, Aug 30,2011 16:55:57
[DHCP IP: (192.168.1.3)] to MAC address 00:01:E6:70:69:6C, Tuesday, Aug 30,2011 16:28:28
[DoS attack: ACK Scan] attack packets in last 20 sec from ip [212.159.15.7], Tuesday, Aug 30,2011 16:08:19
[DHCP IP: (192.168.1.4)] to MAC address 00:1C:23:03:F9:4B, Tuesday, Aug 30,2011 12:46:44
[Admin login] from source 192.168.1.100, Tuesday, Aug 30,2011 12:27:07
[DoS attack: ACK Scan] attack packets in last 20 sec from ip [212.159.15.10], Tuesday, Aug 30,2011 12:19:33
[DoS attack: ACK Scan] attack packets in last 20 sec from ip [212.159.15.10], Tuesday, Aug 30,2011 12:08:01
[Admin login] from source 192.168.1.100, Tuesday, Aug 30,2011 11:03:43
[DoS attack: ACK Scan] attack packets in last 20 sec from ip [212.159.15.6], Tuesday, Aug 30,2011 10:49:09
[Time synchronized with NTP server] Tuesday, Aug 30,2011 08:13:10
[Internet connected] IP address: 87.113.179.243, Tuesday, Aug 30,2011 08:13:58
[Admin login] from source 192.168.1.100, Tuesday, Aug 30,2011 08:12:34
[Internet disconnected] Tuesday, Aug 30,2011 08:07:29
[DHCP IP: (192.168.1.5)] to MAC address 00:24:2B:07:68:E6, Tuesday, Aug 30,2011 06:29:42
You can set the router to email the logs to you if you wish.
I have mine set to email me at 5:00am every day.
If you do choose that option, the router logs are cleared as soon as the email is sent, so you would have to save the emails for record purposes.
You will see from the above log that it can take quite a few minutes for the router to regain an internet connection, even though the BT modem only takes a few seconds (unless it is continually trying to re-sync due to line/connection problems etc.
If you haven't already received it yet, the Netgear router should arrive from Plusnet a day or so in advance of the FTTC installation & give you time to set it up with your own connection details/wireless access & security etc.
Plusnet can also confirm disconnections/reconnections via a chart, but usually only do so if they are trying to monitor your connection's stability etc.
If you choose to use a different router with the BT modem, it should also have its own logging facility.
HTH.
Paul.