REIN is a type of interference that can affect your broadband. This occurs when an electrical device is being used. You may notice disconnections, line errors or, in extreme cases, no connection at all. You will generally see slower speeds, due to line errors caused as BT's systems attempt to counteract the symptoms.
Common causes of this type of interference is caused by, faulty power adapters, street lamps, railway power lines and even Christmas tree lights.
To avoid this type of interference, firstly, ensure that your physical setup is the best it can be, with working micro-filters and tested directly into the BT test socket. Then, process of elimination will help determine what and when the interference is being caused. If after searching for the source, you have still not located where the interference is coming from, you may need to start looking further afield, starting with asking the neighbours.