I think its a great idea.
Would make solving various crimes far easier, will help identify bodies and help various medical issues. Tracking down other people with similar medical conditions etc.
In my opinion all the people against it are either trying to hide something, or are just overly paranoid
Maybe we've just studied some history. "You have nothing to worry about unless you have something to hide" has always meant something very bad is around the corner.
Besides, no-one really means it.
Would you be comfortable living in a transparent house with cameras covering every part of it?
If not, then by your own argument you must have something bad to hide at home and you should be presumed guilty of abusing your children/parents/partner/pets.
Sound fair to you?
It is unarguably true that such things give a great deal more power to the authorities. Maybe they can be trusted with it. What makes you sure that will always be the case? What if, for example, the BNP gain significant power several decades into the future? A lot of letters could be sent: "Your DNA indicates that your ancestry isn't British White enough for our standards. You are encouraged to leave the country." Or a group much worse than the BNP could emerge and gain power.
The system will not work properly and not be properly secure. It's a government project.
The system will be presumed infallible, when it isn't. Wrongful conviction without effective appeal would be a possibility for anyone, including you.
Then there is the inevitable function creep (assuming you believe that the function is supposed to be limited to criminal investigation in the first place).