What exactly did you apply for - a basic payment, Rent Supplement, Mortgage Interest Supplement or an Exceptional Needs Payment? All are part of the SWA scheme.
It would be unusual for an application to take over a month once all requested information had been supplied by you. You should either have been granted a payment or been notified of a refusal. Contact the CWO at the health centre who took your application and ask for an update on the claim.