I'm afraid it is a total nightmare and you have to have the patience of Job.
I have finally just completed the saga and put my new plates on last week. IT TOOK NINE MONTHS and as far as I can see there is no way to short circuit the process. Even from getting the ITV, sending the stuff to Trafico in Alicante and getting the plates took six weeks.
I did have an additional problem because there was a mistake on the UK log book (V5) where the VIN number did not match the one on the car. One digit was missing. The ITV would not accept it or an Export certificate. The only thing they understood was a letter from Swansea acknowledging the error. All this time I was running on green temporary plates.
I had to remove the front chrome bar, the LPG conversion, tow bar and window film simply because they did not have a Spanish Declaration of Conformity (aka homologation) and there was silly me thinking we were all in Europe and what is sauce for the goose should be sauce for the gander. No UK certification seems to be acceptable in Spain.
To anybody else reading this before you start anything ensure your NIE is under 3 months old and renew your Padron. Ensure all your paperwork matches. It would also help if your UK car has current MoT and tax.