141 is a privacy setting for one call, not a way to make a call anonymous. It tells the network not to show your number to the person you're ringing. Everything else about the call - who made it, when and to whom - is still recorded by the networks involved.

Who can see a 141 number

WhoCan they see or trace it?
The person you callNo - they see "withheld", "private" or "no caller ID"
Their 1471 serviceNo - it says the caller withheld their number
Apps that claim to unmask withheld numbersNot reliably for UK network calls; be sceptical
The phone networksYes - the number is passed between networks for billing and regulation
The policeYes, through lawful requests to the networks
Emergency services (999)Yes - withheld numbers are still shown to emergency services

If you're receiving withheld nuisance calls

You can't trace the caller yourself, but you can start the process:

  1. Keep a log of every call: date, time and what was said.
  2. Call your phone provider on the number on your bill and ask about their nuisance or malicious calls service. Providers can investigate calls made to your line, including withheld ones.
  3. If the calls are threatening, abusive or persistent, report them to the police on 101, or 999 if you're in danger.
  4. Meanwhile, reject withheld calls: BT landline customers can do this with Call Protect (1572), and many providers offer anonymous call rejection.

If you're using 141 yourself

Using 141 is legal and common - doctors, social workers and people protecting their privacy use it every day. Someone leaving an abusive relationship, for example, may withhold their number for good reason, which is exactly why the recipient can't simply reveal it. It just isn't a cloak for harassment. Persistently using a phone network to cause someone annoyance or anxiety can be an offence under the Communications Act 2003, whatever appears on their screen.

For whether you can find out the number behind a withheld call without the police, see can I find out a withheld number. Whether 141 still works on today's phones is covered in does 141 still work for withheld.