Over 4,000 English fans went to Moscow for the Group E match.
The five British citizens were hospitalized with minor injuries in two separate incidents in the past 24 hours, embassy spokesman James Barbour said. There were no reports of arrests, he said. The Interfax news agency said two fans were attacked, apparently by Russians.
Interfax also reported that a group of Russians dressed in black attacked English soccer fans at a bar in central Moscow. And Ekho Moskvy radio reported that 20 Russians barged into a bar in another part of the city and attacked foreigners. Several British citizens were injured, the report said.
In recommendations posted on its Web site, the British Embassy advised English fans to "be as inconspicuous as possible," "be sober" and "leave the vicinity of the stadium as quickly as possible after the final whistle."
Riot police and water cannon trucks were deployed for the sold-out game at Luzhniki stadium.
Nearly 100 English fans joined British Ambassador Tony Brenton in a wreath-laying ceremony at the Tomb of the Unknown Soldier at the walls of the Kremlin. The fans left a St. George flag made from flowers along with a card noting the Russian sacrifices in World War II.
"You will find that a lot of English fans have a lot of respect for the countries they play in," one fan, Lisa O'Brian, told AP Television News. "They come out and they want to acknowledge the fact that a lot of people around the world fought alongside at world wars. So England fans are not that bad as people seem to think they are."