An estimated 10,000 fans are expected to travel to Russia to watch England -- who have been drawn against Belgium, Panama and Tunisia in the group stage -- and have already been warned by police not to wave St George flags as they can be deemed imperialistic.
Fans have been warned to be particularly careful in Volgograd, formerly Stalingrad, which hosts England's opening game against Tunisia on June 18, as it is regarded by Russians as a symbol of the Great Patriotic War (World War II) and contains many important memorials.
Russian and English fans clashed violently in Marseille when France hosted the 2016 European Championships.
Russian hooligans posted photos of dozens of "captured" St George's flags after the clashes.
The Foreign Affairs Committee -- chaired by Conservative Tom Tugendhat but made up of lawmakers from all parties -- also called on the Foreign and Commonwealth Office (FCO) to lay out the assurances that they received over LGBT fans' security.
"MPs remain particularly concerned about safe passage for BAME and LGBT football fans who already face additional risks of attack and persecution in a country whose government has taken 'little action to combat homophobia' (FCO's Human Rights and Democracy Report 2016)," read a statement from the Committee.
"The Committee's Report calls for the FCO to set out the specific assurances it has received from Russian authorities on the safety of LGBT fans."
Tugendhat said he and the Committee had not been impressed by the assurances they had been given by Foreign Office ministers.
"Vague reassurances from Foreign Office ministers have not been enough to reassure us that UK nationals will be safe, regardless of their background or sexual orientation," Tugendhat said.
"The FCO should provide as much information to fans as is possible in the short time still available. UK football fans must know how to manage the risks so that they are safe from the fear of violence," added the 44-year-old former army officer.