The answer here lies in both common law and the Police & Criminal Evidence Act 1984 (PACE). The person being arrested MUST be informed "As soon as is reasonably practicable" (Possible) that they are under arrest & what for. A judge, Viscount Simon, once stated that "It would not be desirable" to have any form of cautioning allowed.
PACE reiterates these conditions. In one case (Name escapes me) "I'm going to have to ask you to accompany me to the station" was deemed unsuitable for a lawful arrest (For a drink driver). Equally, another case shows that "You're nicked" and "You're under arrest" singularly are equally invalid.
It is as it is to prevent acquittals on technicalities, and to give suspects their rights. There are no right or wrong scenarios.
although I suspect this question was asked most out of curiosity, if you require, I can provide you with case names and PACE sections for referencing. My notes are elsewhere currently, my apologies...