When the male-only membership of Augusta National took a collective deep gulp and handed over green jackets to two women last summer, the move seemed to have the same kind of earth-shuddering impact not seen since the dinosaurs were flattened by an asteroid.

In many folk's eyes, golf has always had something of a prehistoric image and everybody jumped aboard the bandwagon of equality. "If the golf club in Augusta can admit women, then shouldn't St Andrews?" asked the former prime minister Gordon Brown, in an utterance of political point scoring as the focus shifted to the affairs of the Royal & Ancient Golf Club in the Auld Grey Toon. "If they can do it in South Carolina, can we not do it in Scotland?"

Augusta is in the state of Georgia. perhaps illustrating the frenzy of kneejerk reaction. Amid the backdrop of finger pointing finger and screams of sexism, the R&A drew up the drawbridge and retreated. Last night, Peter Dawson, the chief executive of the game's governing body outside the US and Mexico, emerged armed with his own opinions on a topic that will continue to stoke up heated debate.

With the Open heading for the all-male Muirfield in July, Dawson has been girding his loins for a renewed bombardment on the issue but he was keen to launch something of a pre-emptive strike yesterday.

He admitted the "temperature is changing" among the R&A's 1800-strong membership and conceded that a female member would "change the perception" but Dawson is keen for reasoned debate.

Royal St George's, which will hold next year's British Women's Amateur Championship, and Royal Troon, which annually co-hosts the Scottish Women's Open Strokeplay Championship, are the other two clubs on the Open rota with a male-only policy. Outspoken critics have snarled that such clubs should be stripped of the honour of staging the world's most celebrated major championship but Dawson was quick to close the door on the notion.

"The legal situation is very clear that the Government recognises the rights of these clubs to exist," he said. "To think that the R&A might say to a club like Muirfield 'you are not going to have The Open any more unless you change your policy' is frankly a bullying position that we would never take. We don't see it as our role to attack golf clubs which are behaving legally. Personally, I think this idea that it sends out a dreadful message to the world is considerably overblown, but that is my own opinion.

"My position is that I totally believe in equality but I do also believe that there are times when men need to socialise with men and women need to socialise with women. I think that reflects majority opinion and I don't think there's much wrong with that as long as nobody is disadvantaged by it. I totally understand and respect the point of view that there is a perception problem but I don't actually believe that the Open being played at Royal St George's or Muirfield or Troon does have the negative impact suggested.

"I understand that people might want to be against single-sex clubs but I don't believe that a few single-sex clubs, even if the Open is held at one of them, materially affects participation in the game of golf."

So will the R&A follow Augusta's lead and open the doors to female members? "Admitting a small number of women members, while it would send out a potentially positive message, I don't actually think it would change very much in British golf," he added.

As the game continues on, what Dawson calls, "a journey" to a place where everybody is happy, he believes nirvana can be found on his own doorstep in St Andrews with five clubs – three all-male and two all-female – co-existing in harmony.

"Golf is on a journey. You see articles still banging the drum about notices [at clubs] which said 'dogs on a lead, no women'. First of all, I doubt if that ever existed and, if it did, it was 100 years ago. All that does is stall the direction of travel. The reason female-only clubs were formed was because men wouldn't let them into their clubs. But having been formed as long as they have there's quite a number of women clubs that don't want to change. If you polled women in St Andrews about the R&A allowing women members it would be an overwhelming 'no'. There is no pressure for a mixed-gender club in St Andrews. People are very happy to be able to join the clubs as they are.

"I remember walking here [the Old Course] on the weekend after the Augusta announcement. The Old Course is closed on Sundays and there were 100s of people playing with balls and walking dogs. I thought about Augusta and their security and their high fences and I thought 'who has the greater access?'"