British No 1 believes he can now deal with grand slams as he faces Tomas Berdych for a place in French Open quarter-finals

When Andy Murray walks out on the red dirt of Roland Garros today to confront the Czech Tomas Berdych en route to the quarter-finals, he will move one step closer to where he really wants to be: on the sunlit grass of Wimbledon five weeks from now. It is a weekend that could be the highlight of the British sporting summer.

If England are in the quarter-finals of the World Cup that Saturday and Andrew Strauss's cricketers have continued their renaissance convincingly enough to beat Australia at Lord's in a one-day international on the same afternoon, Murray would hope to find himself on a tidal wave of optimism going into the men's final on Sunday 4 July.

As for the mountainous attention given to football generally and the World Cup in particular, Murray said this month that such obsession will "probably make it a little bit easier" for him to concentrate on his grand mission. He can be sure that if he achieves what no Briton has achieved since 1938, he will for a moment at least put his sport a notch above the God Football.

This, anyway, is the dream scenario for him.

"What's changed with my results in the slams," Murray said last night, "is learning how to deal with difficult situations without panic. I have found ways to come through."

That he has. Getting the nation to grip the edge of their seats seems to be part of the formula as he wrestles with the internal fragility of his own game, not to mention a chronically suspect right knee and the angst he seems incapable of performing without. Murray is a one-man episode of Frasier.

While the fourth seed and British No1 still has legitimate ambitions here, realistically he will do well to reach the semi-finals of an absorbing French Open, where Roger Federer, almost certainly, will stand between him (or anyone else) and the most unlikely of triumphs in a tournament still containing the peerless Rafa Nadal.

Murray will start as favourite today against Berdych to move into the second week of the tournament for a second year running, which would bring him a quarter-final against either Jo-Wilfried Tsonga, the temperamental and physically struggling eighth seed, or the Russian Mikhail Youzhny. The Scot – who has endured an agonising five-setter against Richard Gasquet, a second-round encounter with the awkward Juan Ignacio Chela stretched over two evenings then a mid-match collapse before beating the tough Cypriot Marcos Baghdatis – would fancy his chances against either Tsonga or Youzhny.

Berdych, for one, is an admirer of the Scot. "He's really strong, especially mentally," he said after getting through to the final 16.

"He moves well on court, he can read the game of his opponent very well. He's a really smart player, who can find your weak spots.

"He can also change the rhythm of the game, do something different. Then, when he's a little bit down, he can bring really big serves. And he likes really long, hard matches."

What encourages Murray in his conviction that he is nearing a stage of his career that offers the highest rewards (as opposed to fleeting, teasing hints at them) is his consistent ability to be a contender. Like a hungry prizefighter angling for a title shot, Murray reckons his day cannot be far away. He is also the most astute critic of his own game. He said: "When you go two sets down against a guy like Gasquet, it's very difficult, mentally and physically, to get back in the match. But, if you feel like you have put the work in, you have a chance.

"Also, having variety in your game helps as well. If you can change the way you are playing, play different shots, bring your opponent to the net, or come to the net yourself, or hit the ball flat, or with heavier top spin, those things definitely help. I always had the variety I just didn't know how to use it that well – but, in the last couple of years, I've learned to use it better."

Against Baghdatis, for instance, Murray employed subtle use of defensive strokes from way behind the baseline, looping long, softer forehands to an opponent he could sense was desperate to get to the net the deeper into the match they went. Murray does not lack for patience.

What excites his critics is his apparent reluctance to move out of that seemingly inert mode of passivity, where he gives the impression of doubting his own gifts. He recognises the dilemma, which is why he used his exit game in Doha to experiment with a few daring passages of play, a tactic which brought no little opprobrium down on him. He took the flak well enough.

Now the second week beckons. This is the business end of the tournament. Some of his peers, such as the American Andy Roddick, who went out in a blaze of indifference yesterday, used Paris as a mere training run. Not Murray. His intensity does not allow him such luxury.

"You have to take it one round at a time as so many things can happen in slams, draws can open up, guys can get hurt, or guys can play long matches and get tired and lose matches they shouldn't.

"But the closer you get to winning the event, it becomes more exciting and a little easier to focus. You go on the match court with less doubts than you might do right at the beginning."