Well I applied for mine almost 3 weeks ago. I have been told it could be between 1 & 3 weeks from now. Im going 2 weeks today so its cutting it fine.
The first thing they do is to write to the UK CAA to confirm you have a licence. I thought sending and receiving this would be the part that slows it down but suprisingly it was done by email and the FAA request it same day you fax the forms to them. The CAA will also reply either same day or within a day or 2 as long as you have paid the fee. I would make sure you have sent the form to the CAA and pay the fee by Card and if you fax the forms to the FAA then this first part will be taken care of quickly.
As for the next part I will find out soon hopefully. Thanksgiving hasn't helped. I also then need to arrange an appointment at the FSDO and I dont know how quickly i will get that.