vat on sale of part ex van

I recently part exchanged my van which I bought from new as a non vat registered sole trader so never claimed vat back.  I traded it in to a main dealer and did not charge vat as not registered at that point in time.

They have since sold it as a non vat qualifying vehicle.  On the day I part exed my old van I picked up the new van which I want to claim vat back on, I subsequently registered for vat and back dated it to the day I picked up my new van so the sale and purchase were effectively the same day.   

Does this mean therefore that I should have charged Vat on my old van?

Thanks in advance for any help and advice.