I have seen Ian Hislop list that as one of his greatest failures in an interview. I don't know if they printed an apology and obviously they were dead wrong here, but they (or at least, Hislop) have recognised it as such.
In a review article published in 2010, after Wakefield was disciplined by the General Medical Council, regular columnist Phil Hammond, who contributes to the "Medicine Balls" column under the pseudonym "MD", stated that: "Private Eye got it wrong in its coverage of MMR" in maintaining its support for Wakefield's position long after shortcomings in his work had emerged.
(Separately the writing style is mostly not to my taste, but that's subjective)