Switched over to BT from SKY and I'm pretty much having to do this a few times a day at the moment.
The issue is that my normal connection speed (16) will drop to less than 1 or stop completely.
The only fix is to power off your router at the plug for a minute then fire back up.
Your speed should be back to normal. If it isn't unfortunately you will need to contact BT. Don't use Twitter for this, call. They don't respond to Tweets very well.