Hello, I'm Keith and happy to help you with your question.
I cam only tell you what should have happened regarding your tax bill. It would be normal for a person with an occupational pension to have their personal allowance of 10K applied to that pension through their code number. It is possible that another tax office allocating a code number for the other jobs you have has also given you a personal allowance thus resulting in you underpaying tax. The GBP 1376 you owe you can ask HMRC to recover through next year's tax coding; up to 3K of underpaid tax may be so clawed back. Write to your tax office and tell tham this method of recovery is what you require. The PAYE system actually works quite well to make you tax neutral at the year end, but only if your tax coding is correct. You should always check these as they are issued by tax offices to make sure thay are right as errors can land you in the sort of situation in which you now find yourself.
If you had jobs on top of your police pension then employers should have been deducting National Insurance, stamping your card to use an old expression. It is possible that the remuneration was below the Lower Income Limit of GBP 111 per week. In this case no deductions would have been made which may explain why your contribution record reflects this and you are being refused Job Seeker's Allowance. I would still be worth challenging office who refused you the Allowance explaining your full situation. Do this by letter, not verbally. I always recommend written communication as with verbal there is always the chance that the other party will get hold of the wrong end of the stick if they can even find the stick at all.
I would also suggest that you seek advice and assistance from your local Citizens' Advice Bureau, their experts are particularly well versed in benefit matters.
I do hope I have been able to explain what may have happened and shown you a way forward with your difficulties.