Three Middlesbrough fans were stabbed ahead of the club's Uefa Cup clash against AS Roma in the Italian capital.
The Campo de Fiori is a popular area with British tourists
Cleveland Police said the attack came from an "organised gang of Italian thugs" who targeted two bars where the English fans were drinking.
The violence happened late on Tuesday as about 200 English fans gathered in Rome's central Campo de Fiori area.
British Embassy officials said in all 15 UK fans required hospital treatment for a variety of wounds.
A 39-year-old man who was with his 11-year-old son, underwent surgery in Rome overnight and remains in hospital for observation.
An 18-year-old was also treated in hospital and was expected to be released on Wednesday.
A spokesman for the British Embassy in Rome said five Italians were being held by local police.
Italian officers with batons were brought in to break up the violence.
A spokesman for Cleveland Police, who have officers with Boro fans in Italy, said at one point a lighted flare was thrown into a bar where Middlesbrough fans, some in family groups, were drinking.
He said most English fans fled for safety, but some retaliated and tables and chairs were thrown as the violence worsened.
The spokesman said the injured supporters were aged between 16 and 55.
Supt Steve Swales, Cleveland Police's commander on the Italian trip, appealed for calm ahead of Wednesday's second-leg tie at the Olympic Stadium.
He said: "People back in the UK will be listening to this and watching this during the course of the day. If they are in contact with relatives over here, we would appeal for calm.
"I am appealing for the Middlesbrough people just to take this in their stride, let us and let the Italian authorities deal with the matter.
"A group in excess of 30 Italian youths, described as Italian Ultras, came into the square. They were a clearly well-organised group.
"They had an identified leader at their head - a gentleman who has been described to me as wearing a silver or shiny fireman's-type helmet and a bandana across his face with only his eyes visible.
"These people were carrying sticks, they had axes, we later discovered they had knives, they had firecrackers and paper firebombs.
"The vast majority of the Middlesbrough supporters who were there are what we would describe as good, normal, shirt-wearing supporters of Middlesbrough, not hooligans, not people known for trouble.
"A lot of them were family groups with younger children, some with their wives."
Boro fan John Donovan was in the square when the attack happened. He said: "It was out of the blue and a premeditated attack.
"It was just a case of getting out of there and making yourself as safe as possible."
A group of extremist Roma fans, known as Ultras, are being blamed for the attack. Reports said they were led by a man wielding an axe.
The travelling fans had been warned of possible trouble before they set off for Italy after the club received a detailed briefing from police.
A Boro fan was killed in Amsterdam last year when the club travelled to AZ Alkmaar and there has also been trouble in Ostrava and Zurich.
Brendan O'Connor, 36, of London, had joined friends to travel to Holland where his team were playing Dutch side AZ Alkmaar in November.