Labour’s Luke Pollard also urged Foreign Secretary James Cleverly to apologise for comments which “force LGBT people back into the closet”.
Mr Cleverly previously advised LGBT+ football fans heading to the football tournament to show “a little bit of flex and compromise” and to “respect the culture of your host nation”.
Homosexuality is illegal in Qatar and anyone found participating in same-sex sexual activity can be punished by up to seven years in prison.
It is never acceptable for a Government minister to force LGBT people back into the closet
Foreign Office advice notes “any intimacy between persons in public can be considered offensive, regardless of gender, sexual orientation or intent”.
The tournament kicks off on Sunday November 20, with England and Wales in group B.
Speaking in the Commons, Foreign Office minister David Rutley said: “Ministers and senior officials have raised the concerns of LGBT+ visitors with Qatari authorities at all levels and will continue to engage on this issue ahead of and during the World Cup.
“Qatar has repeatedly committed that everybody is welcome to the tournament and we will continue to encourage equal treatment and the respect of individual rights, and identify what action the Qatari authorities are taking to match their commitment.”
Mr Pollard, the MP for Plymouth Sutton and Devonport, said: “I declare an interest as a massive gay, but as an England-supporting homosexual it is not safe for someone like me to watch the World Cup in Qatar.
“Because of the human rights abuses of migrant workers and Qatar’s LGBT population I personally don’t think Qatar should ever have been awarded a major sporting competition.
“Will the minister back the home nations’ captains in wearing a rainbow armband when they play at the World Cup?”
Mr Pollard went on to ask Mr Rutley to apologise for the Foreign Secretary’s remarks, adding: “Because it is never acceptable for a Government minister to force LGBT people back into the closet.”
Mr Rutley replied: “I respect (Mr Pollard’s) comments and he and I have worked together on many issues in the past and I understand his campaigns on this issue.
“Our priority is, of course, the safety of all British nationals who will be travelling to the World Cup.
“LGBT+ rights is an issue the UK prioritises internationally and we continue to engage with the Qatar authorities on this issue.
“Many sportsmen and women use their platform to do important work across a range of issues, that’s their personal choice.
“The UK Government stands by our values and our teams stand by the values of our home nations.”