Footnote:
In browsing the relevant parts of the gov.uk website, I see how out of date my knowledge has become. "New State Pension" kicks in for men born after 6 Apr 51 and women born after 6 April 53.
It says the page I've linked to, below, no longer applies to them. I include it only because it clarifies what contracting out used to mean. I also learned that contracting out is far from universal among employer schemes and it lists a bunch of public-service sector employment areas as being contracted out.
https://www.gov.uk/additional-state-pension/contracting-out
As far as I can determine, Appropriate Personal Pension (APPs) were contracted out. At least google failed to put any such thing as a "contracted in private pension" as high as page 1. (Note that google cannot handle search terms of less than three letters).
From 6 April 2016, nobody will be contracted out. Some of us are going to see an increased NI deduction on our April payslips. Either I've missed the slew of news stories about thus, or it was wrapped in general budget day hoo-hah, or the publicity splurge will be commencing today.