Closure action varies ...some are lucky enough to receive it in a few weeks, whilst others are taking months and in some cases years. Your IP should be able to give you some indication of the timescales for your specific case.
Sharing from experiences of dealing with debt
There is a solution for everyone .... Just need to stay positive !
I got mine last month, 10 months after my last payment. I was with gt and signed all of the ppi documents so I was involved in the first mass variation meeting which allowed closure while ppi is still being looked in to. Some people seem to get closure with 6-8 weeks, others can take a couple of years. Who are you with?