Thanks for your question. I will try to help.
If you are in the UK and have an old passport with ILR stamped in it as well as a new passport without the stamp then you are entitled to work.
Obviously, you would have to show the old passport and the new passport together but an employer should accept this.
However, for ease of reference you may consider applying for a “no time limit stamp and a biometric residence permit by following the guidance and links on the following page:
Most people have BRPs now and so employers are a bit more used to seeing them instead of the old style stamps in passports.
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I said that you should consider applying for the NTL in my answer above.
If they are saying that you are not permitted to work until you have obtained your NTL then they are wrong.Tom