Recently we were registering a client for VAT. Usually you get the VAT registration number in couple of days.
This time the application did not go through, but HMRC sent a clear and detailed email with the documents required.
We sent those documents but did not hear back for over a week.
I searched for a telephone number and got to the following webpage:
Now they even have a web-chat option and the web chat was very helpful and they gave me a direct number for VAT registration helpline as 0300 523 245.
Good luck !