The R&A is responsible for running the Open Championship which will be held from Thursday at the ancient Muirfield course near Edinburgh in Scotland, one of three exclusively male clubs to host the event alongside Royal St George's and Royal Troon.
Culture Secretary and Minister for Women and Equalities Maria Miller said it sent out the wrong message to hold the Open at a club that did not allow women members. She urged clubs to lift all bans as the number of women golfers declines.
"Sports governing bodies should be doing all they can to promote equality and address the sexism that still exists in some quarters, not turning a blind eye to it," Miller said in statement after turning down an invitation to the event.
Sports Minister Hugh Robertson and Scotland's First Minister Alex Salmond have also rejected invitations to the 142nd Open, the only Major to be played at a single-sex club. The three other Majors are played in the United States.
Salmond, a keen golfer, said it was "indefensible" in the "21st century not to have a golf club that's open to all".
The protests follow a decision by the Augusta National Golf Club in Georgia to end a men-only policy before the Masters in April with former US Secretary of State Condoleezza Rice and Darla Moore, the philanthropist, among its first female members.
Some of Britain's best-known women golfers have spoken out recently against Muirfield, with Vivien Saunders, Catriona Matthew and Laura Davies saying they did not feel comfortable that such a Major sporting event went to a single-sex club.
The Times joined the debate on Monday, with an editorial saying the sport of golf still had a problem with gender and it was time The R&A took "some moral leadership".
But The R&A brushed aside calls for the Open to be taken away from venues with men-only policies and said it had no plans to change single-sex clubs that are allowed under British equality laws as long as there is guest access.
A spokesman for R&A chief executive Peter Dawson said he had made the organisation's views on single sex golf clubs clear at a news conference in April and had nothing more to add.
At that time Dawson stressed that only about one per cent of 3,000 golf courses in Britain used by about 1.3 million players had a single sex membership policy - and some were women only.
"Personally I think this idea that it sends out a dreadful message to the world is considerably overblown," said Dawson who will face the media again at Muirfield on Wednesday.
"I think private clubs can determine their own destiny."
A spokesman for Muirfield, which boasts it is the world's oldest golf club dating back to 1744, said women were welcome to play as visitors or guests year round and use the facilities.
"We are disappointed that some individuals feel unable to attend this year's Open staged by The R&A at Muirfield," the club said in a statement ahead of hosting its 16th Open but added there were no plans for any change.
The Ladies Golf Union, representing ladies' amateur golf in Britain and Ireland, said it boycotted men-only clubs 15 years ago but the ban lasted only three years as it did not help.
"Why should we be denied the opportunity to play some of the best courses in the country so we do now hold championships for women at Muirfield and other men-only clubs," chief executive Shona Malcolm told Reuters.
"But really this is nothing compared to the biggest issue facing women's golf which is a massive 20 percent drop in women players in the past 10 years from 210,000 in 2004 to 177,000 last year. That is far more of a priority for us."
- Sports & Recreation
- Maria Miller