Currently, HMRC are processing requests make on 18 July, so 2 months is normal. I'd suggest waiting a couple of weeks, and if you don't hear from them, then call on 0845 915 4811.
You do need to include both your US Social Security and your UK National Insurance number, and if you didn't, this may cause a delay.
It is generally quicker to apply for the UK/US 1 via fax. The correct fax number is 0191 225 4215.
You need to include your full name, address, NI number and SS number.
From experience, 9 out of 10 times when exemption is claimed from SE tax and the certificate is not enclosed, there are no problems, and the IRS process as normal. Approx 1 out of 10 times, the IRS do insist on seeing the certificate. You may want to file the return now without the certificate, and worse comes to the worse the IRS will ask to see the certificate later.