I think the Justice Minister's reasoning is that if we pardon every crime in the past that we deem permissible today, it would legitimize people to break laws they find unjust today, stating that they (perpetrator) did it "because the future will see it as ok". It feels like weak reasoning from my part, but I can't get into the Justice Minister's head. It's just speculation.
With that said, and Turing having been pardoned by the Queen (posthumously), I wonder if pardons in the UK also carry the "imputation of guilt" that pardons in the US carry as defined by the SCOTUS [0]?
That is what pardons are for. If he was not properly convicted then the conviction could have been overturned instead.