Frank Jane's link does explain the position. The Key phrase is 'contracted out'. I presume that all three of you worked for the same bank and were all 'contracted out' meaning that you paid basic rate NI and your employer credited the earnings related element to your Bank Pension scheme. Then you worked for a different Council from the other two - they were contracted out by their Councils, whilst you were not. Your £20 per week sounds about right for 5 years worth of additional NI on a reasonable salary. I have £60.65 additional pension due to never having been contracted out, my DH has a tiny amount because he was mainly self-employed - additional NI only taken for a few years when he WAS an employee and my retired civil servant sister has none at all (but has a generous civil service pension to compensate) because she was contracted out her entire working life.
Once again I am amazed that you do not know how lucky you are - my DH worked for 52 years to your 38 and has a pittance of a pension compared with yours. 