Once you get your VAT number issued, you need to enter it into Amazon UK.
HMRC will issue you a 9 digit code.
You will need to add GB to the front of the 9 digit code (no spaces) for it to be accepted by Amazon.
If your number is rejected then the VAT databases may not have been updated, so try again a few days later.
You can check your VAT number on the database here: http://ec.europa.eu/taxation_customs/vies/?locale=en