I've grouped your question with two others regarding camping permits. In my response to Krystina's question, I included a link to the site where you can obtain this permit.
You click on that initially and you get a page listing all the campsites. Click next on the "Solicitar Permiso" button.
You then get a screen which says, at the top "Si es la primera vez que solicita una acampada, haga click con el ratón Aquí para registrarse como usuario." This just means, if this is your first time applying for a permit, click here to register. So, you click on "Aqui".
Next, you have the registration form. Here's what you put in the boxes:
NIF o pasaporte - your passport number
Password - just make one up
Confirm password - type it again
Codigo del Municipio - Municipal code (scroll down to United Kingdom)
Nombre - Your first name
Primer apellido - Your surname
Segundo apellido - leave blank
Direccion - Your address
Codigo Postal - Your postcode
Telefono - I'll leave you to work that out
Fax (optional)
eMail (optional)
Then, click on "Registrarse" and you will be registered.
Thereafter, I'm not sure what happens, as I've never registered for a camping permit myself, but if you get this far and then get stuck, feel free to add a further comment to this question, requesting more help and I'll see what I can do.