I passed through Dover Port on Friday afternoon in my car. There were delayed ferries because of the weather though I was put on an earlier ferry as a result and left earlier than booked. The weather was rough but DFDS were coping better than I had expected. There were hardly any delays for cars at the port. The only problems were with trucks getting in the wrong lanes and blocking access to the port and to the check in kiosks. That was being handled by police/port staff.
As for immigration, there was no delays at the French border control and the British BF just waved us through unchecked (back to the good old days!). I did hear that there were 2 hour delays for coaches at the time we went through.