BT BB - dropping connection

ka7e

We've recently upgraded to 8mb with new BT hub (formerly Belkin router) and are experiencing regular disconnections. Strangely, these are at precisely 4pm and 12am and cause the BB connection to drop every few minutes, for up to 2 hours. Meaning we have no usable connection between 4-6pm and 12-2am.
BT wouldn't investigate for 10 days as it said that was the usual "settling in " period!
This week we realised the actual phone connection is affected as well, so we thought it must be a phone line problem rather than a BB one. Actual calls aren't "dropped", but intermitantly, callers get a busy signal when calling in - and we can't dial out. BT tested the line and no fault detected, they are at a loss as to why the line fails at specific times.

So far we have tried;

• resetting the hub - no change
• plugging router directly to phone socket (usually on an extension) - no change
• switching hub off overnight - no change
• disconnecting router at 4pm - phone line is stable! Points back to it being a BB problem.
• trying to locate "master socket" - no luck.
• using old Belkin router - no change.

BT have just called back to ask us to disconnect Sky at 4pm to see if that is affecting the connection (we've had Sky for years with no problem), and to phone for a line test at 4pm. Presumably using a mobile phone!

Has anyone else experienced anything like this? Or could offer an explanation as to why the problem only occurs at such specific times?