s161 Penalties for causing certain kinds of danger or annoyance, Highways Act 1980
... (3) If a person plays at football or any other game on a highway to the
annoyance of a user of the highway he is guilty of an offence and
liable to a fine not exceeding [F3 level 1 on the standard scale]. ...
(See also the s137 offence of wilful obstruction.)
Some places may also have their own related bylaws, e.g.
No person shall on any land adjoining a street play any game in a
manner likely to cause obstruction to any traffic or to cause danger
to any person in such a street
Made under s235 of the Local Government Act 1972, for the prevention and suppression of nuisances.
Traveling further back in time, the Highway Act 1835 provided for penalties on persons who "play at Football or any other Game on any Part of the said Highways, to the Annoyance of any Passenger or Passengers" and, in London, the Metropolitan Police Act 1839 similarly made it an offence to "any Kite or play at any Game to the Annoyance of the Inhabitants or Passengers, or who shall make or use any Slide upon Ice or Snow in any Street or other Thoroughfare, to the common Danger of the Passengers."
I find such a claim implausible, considering the large amount of my childhood that was spent playing in the street with no legal problems.
It seems possible that the authorities turned a blind eye or your behaviour didn't come to their attention, or your street was designated as a 'play street' (introduced by the Street Playgrounds Act 1938, currently provided for by sections 29 to 31 of the Road Traffic Regulation Act 1984 as amended by the New Roads and Street Works Act 1991). Also, many alleged offenders might be younger than the criminal age of responsibility.
According to TJ Miller MP (Colchester) in Hansard, speaking in 1860, in 1859 44 of London's children were sent to prison for playing games in the streets, and by April 1860 25 had been sent to prison - apparently Manchester had imprisoned none.
In my youth we played in the street although we didn't put up basketball hoops, football goals or other such objects. These stories in the media seem to be rare and involve circumstances where the local authority received too many complaints, particularly when there is damage to homes, cars or flowerbeds - which may amount to criminal damage.
Blackpool in 2006
Glenfield area of Leicester, 2007
Newark, Nottinghamshire, 2008
Manchester, 2010 - although this seems to be based on one complaint
Hat-tip Pedestrian Liberation for the information about the older legislation and arrests of children.