The SWA3 form which you downloaded is the most recent - you don't have to get it stamped by the local authority, but you do have to declare whether you've been to the local authority, and whether you're on the housing list or not.
If you've been renting for less than 6 of the past 12 months, and you're not on a housing list, you will have to be assessed by the local authority and put onto the housing list before Rent Supplement can be granted - these are new rules which came in last June/July so you might not have met them last time you claimed.
If you are on the housing list and you have a letter from the local authority to say so, it would be useful to bring it with you - the CWO can copy it for their files.