Hello, I'm Keith and happy to help you with your question.
Unfortunately, all the income you receive is not taxed at source. Just to start with your State Pension (SP), although taxable, is paid gross. What would normally happen is that the pension from another source would have the code number depressed to collect the tax due on the SP. This is very common with occupational pension schemes, but your question clearly states that this is, in your case, a private pension and it might not be happening. So, let us examine your real tax situation. Get a wet towel round your head and the back of a large envelope and make 3 columns, one large and two smaller. In the large one put where the money comes from and in the left hand smaller one the gross amount and in the right hand the tax deducted. Once you have done this for all income including bank and building society interest and dividends, proceed as follows. Total up the two columns. To the left hand one you, from your figures, will have 7593 + 5091 + 94 = 12777. Deduct your personal allowance of 11000 leaves 1777 taxable at 20% = 355 total tax bill for the year.
The total from the right hand column is then deducted from the tax calculated in the left and the sum remaining if positive is the tax underpaid and negative the tax overpaid. The figure you are quoting, 13139 appears incorrect and should be challenged and the subject of an appeal to your tax office which you do simply by writing a letter to HMRC pointing out the error and requesting an adjustment to the correct figures. HMRC may, of course, have been making assumptions. Tax offices are very good at this and in my experience they are invariably incorrect and mysteriously always in favour of the Revenue. An appeal is the route to take.
When you submit your annual self assessment tax return to your tax office HMRC will issue you with a statement indicating the tax over or under paid. The method used is the most convoluted and addled that I have, as an accountant, ever seen, but in the end the result should be the same. The normal procedure is to refund you any overpaid tax as you directed on your return form or reduce your code number in some future tax year to effect the recovery of any tax underpaid. Simple, as the Mercat in the TV advert would say!
You would appear to be correct in your surmise that you are being taxed on more income that you receive, but try going through my method just to check. As in all tax matters check, check and double check, check and check again is the mantra to adopt. Remember that the left hand column figure is the GROSS received.
I do hope I have helped you with your question.