Most beaches in England and Wales are owned by some one, mostly English Heritage or the National Trust and local Councils, all of these have by-laws preventing driving on the beaches.
However in some areas they allow limited access to the beaches with motor vehicles, mostly for on beach parking.
These facilities are few and far between and usually there is a small charge incurred and a strict set of rules about how fast you can drive and where you can drive, these days most are cordoned off in areas.
If you want to drive on a beach please please check the legitimacy and local by-laws or you WILL get a section 59.
Even private beaches are governed by local county by-laws in England and Wales.
Example
http://www.bobw.co.uk/Uploads/CMS/Files ... 0exist.pdf
Enjoy.
http://www.opsi.gov.uk/acts/acts2006/pd ... 016_en.pdf