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Yes this is correct, your tax allowance can only go agaist one job.
Now say you had two jobs each paying £10k. Your tax allowance would still be against one and the other would be fully taxed at 20%. But in this case you have overpaid as you still have £2k of tax allowance unused - this would get sorted out at the end of the tax year when the HRMC will do the tax calculation across both jobs and refund you the over-payment (20% of £2000 = £400).