Tony Blair has said Britons involved in continuing violence in Portugal "bring shame on our country".
Twelve England fans appeared in court on Wednesday
He told prime minister's questions the clashes in Albufeira on the Algarve were "completely intolerable".
Portuguese police said 33 English football fans and one Dutch man, were arrested overnight, adding to a dozen held on Monday night.
England were told before Euro 2004 that hooliganism could see the team sent home, but Uefa has said the recent violence is unrelated to matches.
Mounted officers and riot police clashed with around 250 bottle-throwing supporters in the resort of Albufeira - the scene of similar ugly scenes the previous night and the base for the majority of England fans.
Mr Blair told the Commons: "The police should come down very heavily and make sure that those who engage in this disorder face heavy penalties."
A Uefa spokesman said England's position was not under threat, but said action could be taken if violence spread to matches.
"From our perspective we view it as unrelated to the tournament. It is not being viewed as football hooliganism by Uefa.
"However, if it changes - and we hope it doesn't - and there is trouble around a stadium or around an England match that position could change and we would have to review it."
Twelve fans arrested in the resort on Monday night appeared in court on Wednesday.
They have been charged with public order offences and resisting arrest. They deny the charges.
Three green police vans carried the English fans to court, where a small group of friends and well-wishers had gathered. One shouted "I'm innocent" as he was led into court.
All of the dozen attending court - who were aged between 19 and 46 - were handcuffed. A Russian and a Portuguese man also came to court.
Through the afternoon 20 Portuguese police officers were asked to identify the English suspects and the case was set to continue on into the evening.
All of the English fans charged were offered the choice of a full trial or immediate deportation by the judge. It is understood they are likely to accept the latter.
Ricky Tsigarides, 23, from Cheshunt, Hertfordshire, told the court he had been enjoying a drink with friends and holding a flag, when he was hit twice on the legs by a policeman, knocked to the floor and dragged away.
He said: "My holiday has been ruined because one stupid idiot threw a chair at the police and unfortunately I was in the wrong place at the wrong time."
BBC News Online reporter Duncan Walker, inside the court, said there were difficulties because some felt the translator was "not sufficiently proficient" in Portuguese. She has since been replaced.
He added that some of the fans complained they felt they had not had proper access to adequate legal representation.
England know they could be sent home if trouble continues
Friends of the defendants said they were unable to understand proceedings and feared police could take action once they returned to the UK.
A Home Office spokesperson in London said if there was enough evidence gathered by British police, then any fans deported would still face prosecution in the UK and the possibility of a banning order.
David Swift, the senior British officer advising the Portuguese authorities during Euro
2004, said the violence had nothing to do with the competition.
"What we have is English yobs getting drunk and disgracing the country. The connection with the game is non-existent."
The Staffordshire deputy chief constable said the violence had "racist overtones".