Hello, I'm Keith and happy to help you with your question. The news I impart will not, I feel, be to your liking.
To put it bluntly, because someone in HMRC made errors on your tax code. The routine treatment for people on pension is for their pensions to have a tax code which reflects their personal allowance, currently 10K. If you had other untaxed income eg a State Pension the code number would be adjusted downwards to collect the tax due thereon. I have personal experience of this and once argued with my tax office who insisted that my State Pension was lower than it actually was. After several letters I found that the office in question had assumed that I had a basic State Pension, totally oblibivious of SERPS and the State Secondary Pension, not to mention the old GPC scheme. In 14/15 for the first time in 20 years they actually got it right first time, well nearly.
Having covered that point HMRC should issue a tax code to your part time employer to cover your additional income, either taxing it all at the basic 20% rate or maybe a higher rate. If some clown in your tax office has given you a personal allowance for that too then an underpayment of tax at the year end is inevitable. The PAYE system actually works well to make you tax neutral at the year end, but only oif the tax codes are correct. You should always check HMRC's notification of all tax codes to ensure that errors have not been made and challenge codes which are incorrect.
You should be notified at the end of each tax year of the taxable income, the tax deducted and any surplus or deficiency notified. Up to 2K can be corrected in the next tax year's codings. Do not accept any airy fairy letters telling you that you have underpaid, insist on a full end of the year statement and then check it against your P60s or other records. If it is incorrect, and it very frequently is, then submit an appeal. This is simply done by writing a letter to your tax office querying their figures.
Whichever way the cookie crumbles you cannot escape liability for underpaid tax even if it is HMRC who have made a mess of the PAYE process. You mention the word 'peanalised,' by this I assume you are using it in a general sense not HMRC trying to impose penalties on top of tax genuinely underpaid.
Without a great deal more data I connot tell you why your tax code has doubled, it simply does not sound right. I suspect that someone in your tax office has got it round their neck again. As always it is a case of check, check and double check, check and check again.
I am so sorry to have to rain on your parade.