Flexi-time is not universal in the Civil Service. Some offices have it and some don't. Your statement above is misleading.
Which Departments don't have flexi-time for the relevant grades? I have never come across one that doesn't.
And, as a civil servant represented by one of the Unions that took the issue to arbitration, I think it was a major own goal. It looks ludicrous to the general public that mid ranking and senior civil servants are making such a fuss about a minimum change to their working conditions. I have 31 days leave. That's plenty. I don't need an additional 2 days and neither does anyone else at my grade or more senior grades.