Penalty Kicks – conceived in Sheffield and first awarded in England against Wednesday FC

Like much else in Association football the original concept originated in Sheffield as some kind of punishment for fouls that had caused a goal to be missed . The Sheffield solution was not to award a penalty kick but to award a penalty goal. The concept of a penalty goal for fouls within 2 yards of the goal was suggested at a Sheffield  Football Association meeting in 1879 :
‘.. if a player fouls the ball within 2 yards of his own goal and in the umpire’s opinion a goal would have been obtained but for such a foul, a goal shall be given against the defending side.’
It was discussed at a meeting 18th February 1879 and later rescinded :

Clearly it was felt that awarding a goal was too generous a response and it would be 12 years later before the first incarnation of the penalty kick was introduced on 2 June 1891 by the International Football Association Board.
The new penalty law required new pitch marking. Two lines were marked across the field, 12 and 18 yards from each goal line, replacing the semi-circles that had been in force since 1887. The penalty was not taken from a spot but anywhere along the 12-yard line until 1902. A penalty kick was awarded for offences occurring 12 yards from the goal line. The other players had to stand behind the ball and at least 6 yards from the kicker, as marked by the 18-yard line, when the kick took place.

An excellent explanation with diagram appeared in the Scottish Referee – Monday 03 August 1891

It was one of the most momentous changes to the Laws of the Game, and while the new law was intended for the following season it did not take long to make an impact. The first award of a penalty took place just four days later, on 6 June 1891, at Mavisbank Park in Airdrie.
Scottish Sport reported how Larkhall side Royal Albert defeated Airdrieonians 2-0 to lift the Airdrie Charity Cup, and how one of their players made history. Around 2000 fans ‘witnessed what is in all likelihood the first case of a referee granting a foul under the new law for tripping, holding, or handling the ball within twelve yards of goal. Mr Robertson was referee and decreed against one of the Airdrie backs soon after the start.’
Few people, least of all the players, knew what to expect: ‘That the new law was a puzzle to the players was evident, all appeared think they could stand in front of the ball as of old, but imagine the astonishment of both players and spectators when Connor alone was left between the sticks, while his ten companions had to go six yards behind the ball along with the Royalists. In simple, the new law means that but two men settle such infringement, the kicker and opposing goalkeeper, and a goal is a moral certainty with half good management.’ The writer was prescient enough to see trouble ahead: ‘The new penalty is most stringent, and referees will require to satisfy themselves that the law has been wilfully broken before bringing such penalty into force or we may hear of some ‘scenes’ during the incoming season when cup ties are in full swing, and partisanship red hot.’

With thanks to Andy Mitchell at: http://www.scottishsporthistory.com/sports-history-news-and-blog/born-in-scotland-the-story-of-the-penalty-kick