In a letter to representatives of the online industry Vaizey said changes to website operations will not be expected overnight as the new EU rules on 'cookies' come into force tomorrow.
The Information Commissioner's Office (ICO) said websites will have up to 12 months to "get their house in order" before enforcement of the new law will begin.
The ICO also today published guidance on its approach to enforcing the new rules.
In March the Information Commissioner told websites in the UK to "wake up" to the new EU legislation, which comes into force as an amendment to the EU's Privacy and Electronic Communications Directive.
Under the amendment websites in the UK need to obtain consent from visitors in order to store on and retrieve usage information from their computers such as cookies, which enable sites to remember users' preferences.
Today the government reiterated its point that organisations and businesses should be given time to "come up with workable technical solutions" before enforcement begins.
"We recognise that some website users have real concerns around online privacy, but also recognise that cookies play a key role in the smooth running of the internet," Vaizey said in a release.
"This Europe-wide legislation will ultimately help improve the control that individuals have over their personal data and help ensure they can use the internet with confidence. But it will take time for workable technical solutions to be developed, evaluated and rolled out, so we have decided that a 'phased in' approach is right."
According to the release the government believes default browser settings "do not meet the requirements of the Directive as they stand". A working group has been formed with browser manufacturers to look at the issue.
Outlining the UK's approach to the changes in the letter Vaizey said it does not rule out ways of getting consent other than through browser settings.
"This reflects the position set out in the government response on Framework implementation that we do not think there is any rationale for government to specify the technical measures needed to obtain consent.
"We have made clear that it is industry that is best placed to develop technical solutions that meet the requirements of the Directive. The wording of the UK implementation reflects and enables this."
The letter also discusses in detail the definition of "consent" in the context of the new rules.
"... the word 'prior' does not occur in Article 5(3) of the Directive, and it therefore does not appear in the UK transposition. Crucially, there is no indication in the definition as to when that consent may be given, and so it is possible that consent may be given after or during processing.
"It is important that stakeholders are aware that in its natural usage 'consent' rarely refers to a permission given after the action for which consent is being sought has been taken.
"This absolutely does not preclude a regulatory approach that recognises that in certain circumstances it is impracticable to obtain consent prior to processing. It also supports any approach underpinned by industry's attempts to inform users about the specific choices available and as a result allow users to make choices (ie give consent) based on that information.
"Crucially, the requirement of the revised Directive is for informed consent."
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