Disabled to private.
For taxation tax class changes eg from disabled to private, you’ll need to tax at your nearest DVLA local office (below). Write the new tax class in section seven of your Registration Certificate, and take the fee, current insurance and MOT if applicable.
http://www.dvla.gov.uk/contactus/localoffices/findnear.aspx
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Private to disabled.
Slightly different -- If you’re changing the tax class from private to disabled, provided you have the whole Registration Certificate, you can tax at a main Post Office® branch.
If you only have the New Keeper Supplement and for other tax class changes eg from disabled to private, you’ll need to tax at your nearest DVLA local office (as above). Write the new tax class in section seven of your Registration Certificate. If using a New Keeper Supplement, you’ll also need to fill in a V62 ‘Application for a Vehicle Registration Certificate (V5C)’.
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Your insurance will commence from the time and date you arrange with the insurer, the car must be covered and you must first have the cover note or certificate in order to obtain the tax.
Old disabled tax disc should be kept by the seller of the car, who has to return or surrender to the DVLA
M.I.D is the motor insurers database that Maxsteam mentions up above and kindly placed a link.