Politicians condemned Muirfield's men-only membership policy as the British Open got under way on Thursday at the Scottish course.
Golf's R and A governing body has faced a storm of criticism over the decision to hold the sport's oldest and most prestigious tournament at the coastal venue east of Edinburgh.
Britain's sports secretary Maria Miller is boycotting the event, while a spokesman for Prime Minister David Cameron said he backed her decision.
"The Prime Minister has a great deal of sympathy with the view that exclusive memberships of this sort look more to the past than they do to the future," the spokesman told reporters.
Scotland's First Minister Alex Salmond has also said he will boycott the championship.
The 269-year-old Honourable Company of Edinburgh Golfers club admits women as guests, but not as members.
Deputy Prime Minister Nick Clegg told London's LBC radio: "I'm dismayed the club does not accept women as members. I find that inexplicable in this day and age."
But he added that it was not for politicians to determine where the Open is staged.
In parliament on Thursday, Andrew Lansley, leader of the lower House of Commons - responsible for arranging government business - called the policy "entirely reprehensible".
Meanwhile the opposition Labour Party's sports spokeswoman Harriet Harman called for a ban on no-women sports clubs.
"After the recent successes of female sport it's an embarrassment that this year's British Open, a world class sporting event, is being held at a club which does not admit women members," she said.
"It's time that Muirfield dragged itself into the 21st century and let women in. It's time to ban men-only sport clubs."
Comparisons were drawn with the struggle for racial equality, with one lawmaker blasting what she called the "bigoted bunker mentality" at Muirfield.
The venue is one of three clubs out of the current nine used on rotation for the Open that has a male-only membership policy. The two others are Royal Troon in western Scotland and Royal St George's in southeast England.
But pressure on Muirfield and the R and A was cranked up two years ago when the Augusta National Club in Georgia, which hosts the US Masters, finally opened their doors to women members after years of resistance.
The R and A's chief executive Peter Dawson said of the row at Wednesday's pre-tournament press conference: "I think at the R and A we've been through over 250 years of existence without getting into political comment and I don't really intend to break that rule here."
Players at the Open have been reluctant to answer questions about the issue.
Of the small number of single-sex golf clubs in Britain, around half are women-only, the R and A said.