England defender Danny Rose said he was racially abused and pelted with stones in the southern city of Krusevac before, during and after Tuesday's match which England won 1-0 to qualify for next year's European Under-21 championships in Israel.
Rose has called for Serbia to be banned from internationals but the Serbian FA has denied there was racist chanting at the game and accused the player of behaving in a "vulgar manner" as a brawl broke out on the pitch after the final whistle.
A spokesman for British Prime Minister David Cameron said in a statement: "The Prime Minister is certainly aware of the events.
"He is appalled by the scenes we have seen in Serbia and we are determined to stamp out racism internationally and at home and we are giving our full backing to the FA's complaint on this issue.
"Hugh Robertson [the Minister for Sport] has written to the UEFA president urging them to investigate this issue. We would expect tough sanctions if we are going to stamp out racism from football."
In a later statement, UEFA said it had opened disciplinary proceedings against both the Serbia (FSS) and England (FA) associations.
"Regarding alleged racist chanting, UEFA will instigate proceedings against the FSS over the misconduct of their supporters during and at the end of the match. Proceedings will also be instigated against the FSS for the improper conduct of the Serbia players at the end of the match," the statement said.
"UEFA will also commence proceedings against the FA for the improper conduct of the England players at the end of the match.
"These cases will be discussed on the occasion of the next ordinary hearing of the UEFA Control & Disciplinary Body on 22 November 2012."
Serbia have long had problems with racism and football violence. They were forced to play a Euro 2012 qualifier behind closed doors after fans rioted at an abandoned Italy game in Genoa in 2010.
"It is no good giving derisory fines as have been handed out in the past, it's not good enough that people shake hands and forget about it. We need proper sanctions," Cameron added.
England defender Rose, a Tottenham Hotspur player spending this season on loan at Sunderland, called for the strongest possible action.
"They have to be banned. I don't understand how else they can learn from it. They have to be banned," he told Sky Sports News.
England's goal, which sealed a 2-0 aggregate win, came with the last kick of the game at the end of stoppage time and fighting broke out immediately after the final whistle between players and officials as the England players were celebrating.
Rose, who was shown a red card after the final whistle for seemingly kicking the ball away in an aggressive manner, said he was racially abused throughout the evening with the insults beginning before the match even began.
"The monkey chants started straight away while we were warming up. I asked the lads if they could hear it and they said
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