Sink and Washine machine drainage problem

Kitchen sink and washing machine drainage seem to be connected, and not only is the sink extremely slow to drain despite using de-blocker, but the water level rises when the washing machine runs. Also, the washing machine frequently says it is finished when clothes will come out soaking, with water in the bottom of the drum. I opened the washing machine today to have to shut the door immediately to stop the water gushing out and flooding the kitchen floor. Any help would be very much appreciated. Thanks, Rosie