I am in the SN3 area and like yourself I had problems with my modem constantly rebooting.
This went on for 2 weeks and after numerous calls to tech support it was widdle down to low power signal. A engineer was booked to check the line and the modem. Engineer didn't turn up. Back onto tech support and was told that due to recent upgrades the booking never went thru. Meanwhile my connection went down completely with just the receive light blinking so onto tech support again and by this time, I am not in a very good mood and totally hacked off.
Spoke to helpful chap at TS and he put me thru to the faults dept and booked an appointment for engineer to come out, 2 days from call which I could tolerate.
Took that day off work, doorbell rang in the morning, got up, showed the engineer the modem and to my total disbelief the modem was working!!!
I felt like a proper charlie as if I had been lieing but he checked it anyway and got all positive results and since then (2 weeks now) my connection has been fine.
Very strange!