@Richie. Hopefully 2 days to approval then it goes to print almost same day, gets printed in day or 2. Unless case is complicated and they need more information. I think most adult renewals with old passport submitted have no issues
In my case. After “ we have dispatched your passport” no news, no tracking number from DHL ( I think they use TNT for within UK, DHL for overseas ( may be TNT for within EU,may be DHL for rest of the world not sure). May be it will show up at my doorstep without any tracking number details