We need a state second pension scheme on similar terms to public sector pensions, that anyone in employment can pay in to. So if you pay 9% of your salary in (have it deducted at source) the state notionally contributes a proportionate amount to a defined benefit scheme that provides benefits on the same basis as an NHS pension. In the first term of the Blair government Frank Field wanted to introduce something like (similar to what France has) that to provide everyone with the opportunity for a decent retirement, but got overruled by Gordon Brown, who also mounted the great dividend raid that slashed the annuity that my uncle, a self-employed carpenter, was able to buy from his private pension fund by a third (back in the days when you had to spend the fund on an annuity very quickly after retirement, that was an awful system).
There is also the fact that until 2015 people born before 1951 would have been contributing to SERPS or SSP until retirement age, and (significantly) increased their pension entitlement that way. There is no state second pension scheme now and my contributions to SERPS/SSP until it was withdrawn entitle me to a £30/week uplift on my state pension when I eventually get to retirement. My dad got more from his SERPS than from the state pension,