There is a campaign to "Pardon" Alan Turing the mathematician, code-breaker and pioneer of computing. Though that is really the wrong word. He did nothing that we would now consider wrong. Really it is a matter of the authorities admitting they were wrong.
There was a programme on
Channel 4 about this campaign, with comments from Richard Dawkins among others.
If there is to be an apology it should be for everyone affected by the laws against homosexuality in that period, in the same way that there have been apologies about the slave trade. This would just be an acknowledgement that the Zeitgeist has moved on, and we have become more enlightened.
There is a petition on the No 10 website.