Thank you so much DF. I took it into my head (before anyone had replied) and rang the TFL "ULEZ Team" on 0343 222 2222. I spoke to a guy called Lee and explained my predicament. I also gave him the old car reg. He confirmed the car is compliant by the old reg. He said the system struggles to "read" private plates. All I needed to do was send in photos of the V5C (no COC) and email to
[email protected] and the private reg will get added. Takes a couple of days.
Thanks for everyone's help. I'll update this post when it happens or I get an email.