Prime Minister David Cameron was "appalled" at the ugly scenes at the end of the under-21 match between England and Serbia, despite the Serbian authorities insisting there was no racism.
The Government is giving its full backing to a Football Association complaint over alleged racist taunts, and sport minister Hugh Robertson has written to Uefa president Michel Platini urging an investigation, the Prime Minister's official spokesman said.
The Serbian FA has denied any form of racism occurred at the match in Krusevac on Tuesday night and said England player Danny Rose behaved in an "inappropriate, unsportsmanlike and vulgar manner" towards their fans.
Britain expects "tough sanctions" if racism is proved, said Mr Cameron's spokesman.
"He was appalled by the scenes that we have seen in Serbia. 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.
"Clearly it is for Uefa to investigate this issue but we would expect tough sanctions. If we are going to stamp out racism from football, then it is no good giving derisory fines, as have been handed out in the past.
"It is not good enough to say that people should shake hands and forget about it."
Rose complained of racist abuse, including monkey chants, during the Euro 2013 play-off and said he was also hit by missiles thrown from the crowd. The Tottenham defender, on loan at Sunderland, was sent off after the final whistle for kicking a ball in anger as scuffles broke out involving Serbian supporters, players and officials.
Uefa have charged the football associations of both England and Serbia following Tuesday night's events.
The Serbian FA has been charged with alleged racist chanting by fans, and both associations over the behaviour of players at the end of the stormy encounter.