PM agrees with Nick Clegg that clubs such as Open venue are out of step with times, while Harriet Harman calls for a ban

David Cameron led senior politicians in criticising Muirfield's male-only membership policy as the prestigious Open Championship began at the historic course.

The prime minister's spokesman said Cameron had a "great deal of sympathy" with the view that such policies "look more to the past than they do to the future".

Nick Clegg expressed his dismay that Muirfield club, still excludes women from becoming members, while Labour's Harriet Harman called for a ban on male-only clubs.

The prime minister's spokesman said Cameron was not attending the Open and "entirely understands" why Maria Miller, the culture secretary, was not going.

Asked about all-male clubs, he added: "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."

While speaking on his weekly LBC show Call Clegg, Nick Clegg said: "I was just dismayed and incredibly surprised to hear this still goes on in this day and age.

"I find it so out of step with everything else that's happening in the rest of society. It just seems so old-fashioned and so anachronistic to just have a golf club saying that just because you are a woman you can't be a member of that club.

"I think many people will just shake their head and say: 'How on earth is this still possible in this day and age?'"

He added: "I'm dismayed the club does not accept women as members. I find that inexplicable in this day and age, I really do."

Harriet Harman, the shadow culture secretary, went further than Clegg in calling for golf clubs to be ordered to admit women by law. They are currently exempt from Equality Act. She said: "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.

"It's time that Muirfield dragged itself into the 21st century and let women in. It's time to ban men-only sport clubs."

The culture, media and sport secretary, Maria Miller, is boycotting the Open over Muirfield's refusal to admit female members. The sports minister Hugh Robertson and Scottish first minister, Alex Salmond, have also said they will not be attending the event.

Shona Malcolm, chief executive of the Ladies' Golf Union, accepted having men-only clubs was a "bit of an anachronism in this day and age" but said the sport was in an "evolutionary process".

She said any change away from single-sex clubs had to be supported by the sport, and should not be imposed from outside.

She raised the issue the day after Peter Dawson, the chief of golf's governing body, the Royal and Ancient Golf Club, said officials were "very conscious" of views on the issue.

Malcolm told BBC Radio Scotland's Good Morning Scotland programme: "I suppose it's a bit of an anachronism in this day and age that there are single-gender clubs in any sport, not just golf.

"But on the other hand we have a number of affiliated bodies who are single-gender ladies' clubs. They are very traditional, very historic clubs, as are some of the men's ones, and they want to protect their traditions and history as much as the likes of Muirfield does. Some of these clubs are 120 years old."

When asked if it was time for change, she said: "We're in an evolutionary process, freedom of association is one of the cornerstones of our democracy and really we need to respect that, but in this day and age things will move forward with time.

"But it has to be with the members of clubs recognising the benefits of it, wanting to move forward and wanting to embrace change. I think it's much better coming from within the sport than being imposed from outside."

Muirfield, in East Lothian, has been home to the Honourable Company of Edinburgh Golfers – one of the oldest clubs in the world – since 1891.