It wouldn't be January, as the exemption comes in from April Fools Day............
The Budget statement was:
"2.148 VED: classic vehicle exemption – The Government will extend the cut off date from which classic vehicles are exempt from VED by one year. From 1 April 2014 a vehicle manufactured before 1 January 1974 will be exempt from paying VED. (Finance Bill 2014)"
There's currently nothing on the Government sites about applying for the exemption.
I would expect you have to apply for a refund of any existing tax after 1/4/14 and apply for an historic tax disc at the same time. If they are being mean, you might not be able to get a refund, but hopefully no-one's thought that was a good idea!!