Hi nappis!
We sent our passport application for our lil Lewis to the uk and the passport arrived back after 10days-was shocked but very impressed:) it arrived back at end of may. You may encounter a slight delay if the British 'last minute holiday passport panic' hits for July but generally I was very impressed. If you keep an eye on your credit card/debit card, you'll see the payment taken and then I think it's not long after that its sent back.
Good luck:)
Max