I see you're in Essex, out of curiosity what exchange are you connected to? Had this happening to me at the Rainham exchange in Essex also, but o2 and BT kept chucking me to the other, no one wanted to accept the blame. Moved to BT and they fixed the line, seems it was faulty equipment at the exchange.
You can check what exchange you're connected to and what LLU/fibre is avaliable to you here: http://www.samknows.com/broadband/broadband_checker
Sky LLU would be a decent alternative.
have they had BT out to check the connection your end ?