Taxing a car after purchase

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you are supposed to tax it before driving it away as this proves you have insurance too,

Since when does it prove you have insurance?

From December 2013 the insurance check is no longer part of the vehicle taxing process. However you may need your insurance certificate if you're planning to tax your car at the Post Office. It is possible to tax your vehicle either online at www.direct.gov.uk/taxdisc or by phoning the DVLA directly on 0300 123 4321.