My standard renewal application to Peterborough is now completed:
Application made: 28 April
Old passport received at Peterborough: 29 April
Application being processed: 12 May
Application approved: 3 June
Passport printed and sent: 4 June
Obviously I have to wait for it to arrive now, but as far as I can see processing time has reduced to about three weeks. Once approved it seems to be by the next working day that the passport is printed and sent out. It would seem that another 2-3 days elapse before delivery.