BT should let you leave the contract freely if you complain.
Just to check what speed are you syncing at when you have these issues and are you using Ethernet?
Edit: the general good news with BT is that congestion does get fixed almost always, it just takes time, usually around 3 months based on other cases.
It does seem strange for a fibre connection with BT to have congestion, I do not know if you're aware of this, but the fibre cabinet does not go back to your local telephone exchange on fibre. It goes back to a master exchange which will serve multiple telephone exchanges. Hence congestion if it exists will affect usually many thousands of users at once. This is why we don't usually see it on fibre services. If you PM me I can give you an email of the Newcastle based support team who are the best you'll get in BT.
Edited by ukhardy07 (Mon 05-Sep-16 07:24:59)