Enhanced Rate For Mobility And VED

I wonder if anyone else has come across this problem:

I have just spent the last 20 minutes or so waiting in a DVLA phone queue - I've given up in the hope that someone on these forums may be able to help.

My daughter has just received Enhanced Care & Mobility Rates on her PIP, this now, (at long last), entitles her to both blue badge and Free VED, my question is;

How does the free car tax work if your vehicle is already part way through it's tax year?
I have read the site and it talks about what to do when buying a car, taxing it for the first time etc, but nothing regarding what to do when you already have the vehicle taxed and on the road?

Can anybody advise me please?

Wonderful, thanks very much