Incorrect - detained migrants aren't allowed to work due to a government decision, even if they had a work visa when they entered the country legally. Working used to be allowed if the border force failed to decide whether someone was a refugee in good time.

If it's easy to do, please cite your source.

Your assertion that holding a passport from a non-war-zone country makes a claim false is simply false and you can realise this by considering two examples: first, someone from a former war zone who aided the British Army; secondly, someone from a minority the UK recognises as persecuted by their government, such as a Bahá'i in Iran even when it wasn't at war.

Easy to do

Cool. So let's see the source.