Bear in mind how useless UK PLC is at protecting your information - lost laptops, anyone-can-search-and-find etc.
How long before NHS or BUPA have access and are excluding you from healthcare? etc
If the DNA is held as a signature (a bit like an RSA key, based upon your real data, but the real data is never held) then I'm all for it - but if UK PLC wants to keep a copy of my full DNA then no.
Either way, the government will **** it up, guaranteed.