Approved today checking online. Lodged Wednesday 16th October approved Friday 15th November (30 days)
Still have to wait for amended paper license to be sent out (hoping some time next week)
So I was on the money when first guessed would be 4 to 5 weeks.
Hopes this helps for anyone wondering time frame for addition application.
Mine was for Cat A and Cat B (2 rifles) with property letter support with an existing H class license for many years through club.