All I've seen is a copy of the Budget Report and a transcript of the Chancellor's Speech but neither of those mention anything about "nearly new" only "new" vehicles. He said the Secretary of State for Business would announce further details later but I haven't seen anything.
Yep, only applies from mid-May to cars over 10 years old and only when buying new cars:
The rules of the vehicle discount scheme
The vehicle you trade in and the new vehicle you want to buy must meet certain conditions for you to be able to get the discount.
Your vehicle
The vehicle you are trading in must:
* be a car or small van weighing up to 3,500 kilograms (kg)
* be first registered in the United Kingdom (UK) on or before 31 July 1999
* either be registered or have a SORN (Statutory Off Road Notification) with the Driver and Vehicle Licensing Agency (DVLA) in your name
* have been registered to you continuously for 12 calendar months before the order date of the new vehicle
* have a UK address on the registration certificate (V5C)
* have a current MOT test certificate before date of order for the new vehicle
The new vehicle
The new vehicle you want to buy must be:
* a car or small van weighing up to 3,500 kg
* first registered in the UK on or after mid May 2009
* declared new at first registration in the UK with no former keepers