The law on taking DNA samples means that at present the government get to keep records on everyone who is ever arrested regardless of whether they are ever charged or convicted of an offence. This is so obviously unjust that it is hard to see how it remains legal. Having said that it is clear that the DNA database is an incredibly useful tool for legitimate policing functions that it is clearly useful that a DNA database exists, although not as some rather authoritarian police officers are suggesting a universal and compulsory one. Simply abolishing it as is proposed here by the Libertarian Alliance is not going to happen and it isn't particularly desirable in any case, I want the police to have access to the DNA records of violent criminals.
So if forcibly taking DNA samples of innocent people is unjustifiable yet a large database is desirable then another means is going to be needed. Offering people a cash sum in return for them providing a DNA might be the solution, if a price of say £1000 was offered for a sample I'm sure the take up would be vast. The objection to this would be that criminals won't be stupid enough to take part, but actually criminals are generally quite stupid, in want of cash and poor at thinking through the consequences of their actions so this isn't a problem. Criminals themselves don;t even need to sign up as long as their close relatives do.