YANBU for thinking that you're probably going to get shafted, and it's not your fault. We all are, public and private sector alike.
I think, as bellisima says, that the problem isn't so much in the south east (where public sector workers are probably underpaid) but in the regions, where tbh, a public sector job - certainly in one of the areas under central government control - tends to carry a very much pay and benefits package than the private sector and distorts the jobs market.
And as an aside (sorry, am a pensions geek in real life), 6% of salary or even 11% of salary isn't that much to pay for a final salary pension. The rule of thumb in the good times when annuities were cheaper and investment returns better was that you'd need to pay the equivalent of half your age as a percentage of your salary to get a pension of 1/60 of your salary (or, for some schemes like the local government one, 1/80 plus the 3/80 cash grant) payable at state pension age - so around 66 or 67 for most of us. It's probably worse than that now, plus an awful lot of the public sector pension schemes pay out a lot earlier than state pension age - for every five years earlier than state pension age, you'd need to increase the contribution rate by about a third.
But the real problem (sorry, long post, told you I was a geek) is that the rules are different for public and private sector pension schemes. Private sector schemes needed to make sure that they were well funded, ideally to be able to buy, with an insurance company, all the pensions that had been earned at a given date. That's one of the things that killed private final salary pensions. The same rules don't tend to apply to most public sector schemes - even the ones which are backed by a fund of money don't need to practice the same financial prudence that the private sector ones do, and the real biggies, like the principal civil service scheme, the teachers' scheme, the NHS, police and fire schemes don't have a fund at all. You might contribute, you might think you're paying for it, but in fact the pension is paid out of taxes after you retire and your and your employer's contributions don't come close to paying the real cost.
Could go on for days about this, but kudos to anyone who's already made it this far!