It's definitely true (I used to be a UK cop). While there are situations where you can de-arrest someone after arresting them, it's rare, and you do not need to place someone under arrest to detain them. Many (minor) crimes are not "arrestable" offences, for instance a cop cannot arrest you for littering. However he can detain you while he ascertains your identity in order to issue you with a fixed penalty notice (ticket), after which you are free to go and have not been arrested/de-arrested, merely detained. If you refuse to co-operate by giving your details, or he believes you may have given false ones that you can't back up with ID, he can then arrest you under PACE regulations and take you to the station to confirm your identify. But he can't arrest you for the littering. But he can detain you briefly.
On the police shows you mention, when the officer stops a car and takes the person into theirs to check their driving license, search them etc. they are detaining them. Only when they tell them they are under arrest are they actually under arrest, and they need reasonable grounds to suspect them of an arrestable offence before they can do that.
On the police shows you mention, when the officer stops a car and takes the person into theirs to check their driving license, search them etc. they are detaining them. Only when they tell them they are under arrest are they actually under arrest, and they need reasonable grounds to suspect them of an arrestable offence before they can do that.