Gov site states I have 42 years full contributions.
In that case, there is no benefit from making more contributions.
I went through this and they would not tell me the calculation.
But it seems to be:
Assume maximum pension is £100, earned after 35 years of contributions
Is paid at £100 divided by 35, per year.
We were contracted out, but no idea how long for.
But if you were Contracted Out for ten years, they subtract 10 from 35 and pay you 25 years worth.
Even if (and this is important) you actually worked and paid full NI (contracted in) for more.
So you could have worked for 50 years, contracted out for 10, and they will still deduct 10 from the maximum 35, and pay a pension calculated on 25 years contributions.
They will not pay you more than (35 minus 10) 25 years worth, however much you contribute.
You might have some extras from old schemes like Graduated Pensions to be added on.
However
Your Private Pension scheme had contributions during your contracted out years. These funds will (should) have grown over time, and with luck might be big enough to pay you a private pension equal to, or bigger than, what has been deducted from your state pension. If you are unlucky, not so much.
If you are in a position to make contributions, you can pay them into a private scheme. If you are not working, you are only allowed to pay £2880 per year, and the scheme will receive a tax rebate increasing it to £3600. Even if (and this is important) you are too poor to pay tax.
If you are working, you can pay in any amount up to your earnings (there are limits for high earners).
If you know the value of your private pension fund, you can estimate the income it will bring from annuity tables. I usually prefer income drawdown to an annuity.