Just for info:
Each government department and/or agency (such as the Department of Health, H M Passport office or the DVLA) used to have its own website but still with a URL ending in 'gov.uk'. Then someone decided to bring everything together under the 'Gov.uk' banner, so that there's a common layout used throughout. (That, incidentally, has been a total disaster, in my opinion. It's now far harder to find accurate information quickly).
The link given in Barry's post is the old DVLA web address. i.e. it was perfectly genuine but has now been superseded by the links provided by others on this thread.