Many thanks for all the replies.
I was not aware that the reboot is triggered by BT/OR I thought it was initiated by the router itself!
Opinions vary, but most people seem to think the Home Hub 4 is rebooted every 14 days via local trigger. Someone here left it unplugged for 14 days and still observed a reboot, I believe.
That's what I meant, I was referring to. it wasn't due to an issue with noise etc, going by my logs below you can see its being rebooted:
08:48:51, 11 Oct. ( 137.160000) CWMP: session completed successfully
08:48:50, 11 Oct. ( 136.810000) CWMP: HTTP authentication success from https://pbthdm.bt.mo
08:48:22, 11 Oct. ( 128.830000) NTP synchronization success!
08:48:17, 11 Oct. ( 123.370000) CWMP: Server URL: https://pbthdm.bt.mo; Connecting as user: ACS username
08:48:17, 11 Oct. ( 123.360000) CWMP: Session start now. Event code(s): '1 BOOT,4 VALUE CHANGE'
08:48:16, 11 Oct. ( 121.910000) NTP synchronization start
08:48:13, 11 Oct. ( 119.320000) PPP IPCP Receive Configuration ACK
08:48:13, 11 Oct. ( 119.310000) PPP IPCP Send Configuration Request
08:48:13, 11 Oct. ( 119.300000) PPP IPCP Receive Configuration NAK
08:48:11, 11 Oct. ( 117.140000) PPP IPCP Send Configuration ACK
08:48:11, 11 Oct. ( 117.140000) PPP IPCP Receive Configuration Request
08:48:10, 11 Oct. ( 116.630000) PPP IPCP Send Configuration Request
08:48:10, 11 Oct. ( 116.630000) WAN operating mode is DSL
08:48:10, 11 Oct. ( 116.630000) Last WAN operating mode was DSL
08:48:09, 11 Oct. ( 115.160000) PPPoA is up - VPI: 0, VCI:38
08:48:09, 11 Oct. ( 115.140000) CHAP authentication successful
08:48:08, 11 Oct. ( 114.830000) CHAP Receive Challenge
08:48:08, 11 Oct. ( 114.830000) Starting CHAP authentication with peer
08:48:08, 11 Oct. ( 114.830000) PPP LCP Receive Configuration ACK
08:48:08, 11 Oct. ( 114.820000) PPP LCP Send Configuration Request
08:48:08, 11 Oct. ( 114.820000) PPP LCP Receive Configuration Reject
08:48:08, 11 Oct. ( 114.820000) PPP LCP Send Configuration ACK
08:48:08, 11 Oct. ( 114.820000) PPP LCP Receive Configuration Request
08:48:08, 11 Oct. ( 114.680000) PPP LCP Send Configuration Request
08:48:05, 11 Oct. ( 111.540000) ETHoA is up - VPI: 0, VCI:35
08:48:05, 11 Oct. ( 111.540000) DSL is up
08:48:04, 11 Oct. ( 110.470000) DSL noise margin: 5.90 dB upstream, 6.00 dB downstream
08:48:03, 11 Oct. ( 109.460000) DSL line rate: 1108 Kbps upstream, 6453 Kbps downstream
08:47:47, 11 Oct. ( 93.320000) CWMP: session closed due to error: No response
08:47:47, 11 Oct. ( 93.310000) CWMP: Initializing transaction for event code 4 VALUE CHANGE
08:47:47, 11 Oct. ( 93.300000) CWMP: Server URL: https://pbthdm.bt.mo; Connecting as user: ACS username
08:47:47, 11 Oct. ( 93.290000) CWMP: Session start now. Event code(s): '1 BOOT,4 VALUE CHANGE'
08:47:16, 11 Oct. ( 62.810000) CWMP: session closed due to error: No response
08:47:09, 11 Oct. ( 55.650000) CWMP: Server URL: https://pbthdm.bt.mo; Connecting as user: ACS username
08:47:09, 11 Oct. ( 55.650000) CWMP: Session start now. Event code(s): '1 BOOT,4 VALUE CHANGE'
08:47:08, 11 Oct. ( 54.840000) CWMP: Initializing transaction for event code 1 BOOT
08:47:06, 11 Oct. ( 52.010000) Wire Lan Port 1 up
08:47:04, 11 Oct. ( 50.530000) WAN Auto-sensing running.
08:47:01, 11 Oct. ( 47.690000) System up, firmware version: 4.7.5.1.83.8.130.1.26.1.1 (Type A)
08:46:35, 11 Oct. ( 21.670000) System start
08:46:12, 11 Oct. (1273027.310000) PPP LCP Send Termination Request [User request]
08:46:10, 11 Oct. (1273025.360000) The system is going DOWN for reboot.
08:46:10, 11 Oct. (1273025.360000) OpenRG is going for reboot by IPC command
08:46:05, 11 Oct. (1273020.360000) OpenRG will go down for reboot in 5 seconds
It doesn't even check if the connection is being used or not before it starts the reboot process.
Basically its an internal procedure call (IPC) that gets called every 14 days to reboot the HomeHub, so maybe what BT told me was correct in a way, where it is to keep the HH stable.
Very frustrating.
Like I said I am very tempted to use my FRITZ!Box, shows loads more stats and seem to have more control over the connection, but most due to the more info

.
Paul