The Vagrancy Act of 1824, informally called the "Sus Law", allowed police officers in England to stop, search, and even arrest anyone they liked on the basis of suspicion alone. The Act, the short title for which was "An Act for the Punishment of idle and disorderly Persons, and Rogues and Vagabonds, in England", did not apply to Scotland.
Though the law was repealed in 1981 due to extreme resentment culminating in a riot inspired by gratuitous use of the law, it remains part of the English cultural consciousness, to the point that an entirely reasonable element in (especially lighter) television shows is that a person can be arrested for "acting suspiciously". Given the predilection toward quirkiness among the sector of the British public appearing in television shows, it is a bit surprising that the British police ever have any time to arrest actual criminals. If you believe the Daily Mail, they don't.
When one is arrested for "behaving in a highly suspicious manner", the usual recourse is to have someone respectable call the police station and "vouch" for the arrested one. Apparently, under English law, acting a bit odd is an arrestable offence, but proving that you have at least one friend will exonerate you. If said friend happens to be angry at you, they may have the inspired idea to deny knowing you to the police - in fictionland, they will face absolutely no repercussions for lying to the cops in order to get some petty revenge on a friend.
Outside of children's television, this trope is basically unheard of in the United States, possibly because Americans have enough cultural awareness of police abuses to put this beyond the Willing Suspension of Disbelief: that sort of thing is considered either to cross the line into fantasy territory (The Simpsons, for example) or to be a genuinely sinister situation on U.S. TV, but not across The Pond. Meanwhile, in 2008, at least two UK political parties are promising to free the police of accountability and restore their power to arrest whomever they don't like whenever they like.
In American constitutional law, police can stop a person and frisk for weapons based on a "reasonable suspicion that criminal activity may be afoot" (a so-called Terry stop). To do a more thorough search, they must have probable cause and arrest the person, or else get consent.
