At the moment we cannot give you a guesstimate as there is a severe backlog.
Make sure you send your form off by recorded delivery, after two days check on line if it has been delivered and signed for, then contact DWP to check it is in their system.
DWP may be able to give you an idea but usually they will tell you 6 -8 weeks to get an assessment but again this will vary across the regions, some members have had their assessment after a few weeks.
Gary
Nothing on this board constitutes legal advice - always consult a professional about specific problems