Leighton Baines is remembering his teenage days paying the 50p bus fare from Kirkby to Goodison Park in the hope he might get lucky. "I never had a ticket for the match but there would be lots of kids who just hung around," he recalls. And they were streetwise. Ten minutes before the end of every match, the gates would open to let the early leavers beat the rush and that was the moment Baines and his mates had their chance to sneak in "hoping to see big Dunc". And big Dunc, as every self-respecting Evertonian knows, is Duncan Ferguson. Baines's boyhood hero. "He was the one who could change the atmosphere in the whole ground."

It does not take long in Baines's company to understand that Everton's left-back has an almost old-fashioned affinity to his club. "I spoke to Paul Jewell a month ago," he says. "He was Wigan manager when I was there and he could remember asking me in my final season where I wanted to go. I just said 'Everton' immediately. It stuck in his mind because he didn't know why I was so focused on that idea. But I just always had the feeling this was where I belonged."

It is why there was no public fuss from Baines when Manchester United came calling last August and Everton pulled down the shutters. He was tempted, naturally, and flattered that his former manager, David Moyes, wanted to continue their working relationship. Yet Baines has always been a snug fit at Goodison. And, besides, everything has worked out pretty well after all.

Baines, it was said, needed to switch to Manchester if he wanted to play in the Champions League and take over from Ashley Cole in the England side. Yet it is Everton, not United, competing for the top four when Moyes returns to Goodison , with a nine-point gap between the sides and a 37-point swing since the corresponding stage last season.

With four games still to play, Everton have already won more points than ever before in the Premier League era. Baines has been instrumental to it and the long, fascinating battle with Cole – the rival he describes as "robotic" because of his sustained brilliance – appears to have been settled in his favour. Baines will almost certainly be in the team to face Italy in England's first World Cup game on 14 June.

He has certainly had another accomplished season, in direct contrast to the way Cole has been marginalised at Chelsea, and it is also very clear he is enthused by the new style of play that has put the club on an upward trajectory since Roberto Martínez replaced Moyes. Baines, to the question of why he signed a new five-year contract in January, cites the Spaniard before anything, or anyone, else. "The two managers are totally different, in every way," he explains. "They both have things they are really good at but with the current manager, he's ultra-positive. He takes the positive from every single scenario.

"That's been the big thing for me: the difference in the style of play, committing to that and not feeling like we have to adapt to the opposition. The new manager has that confidence and belief in himself, in his own blueprint. And then in us. He tells us we're not going to change, we're just going to improve constantly and keep practising until we get to the level where we want to be. Stick to it, don't compromise, get better at it.

"He also spoke about the Champions League from the start. He didn't shy away from it. He came in and straight away he set the bar high. We might have got away with a fairly ordinary season – the changeover with the new manager, the first season, a transitional season – but he didn't want to accept that. He wanted to improve on what we'd done before, and we've done that."

The Martínez way has meant Baines having to adapt his role. "It's very different. The full-backs at Everton are more advanced now. If [the goalkeeper] Tim Howard has the ball, I'll be encouraged to be higher up the pitch and that creates more space for the midfielders. We can then start our play, building up from the back.

"People will say there's a risk involved, and there are times, as a defender, when I'm one side, Seamus [Coleman] is on the other, and I'm thinking: 'I could do with being 15 to 20 yards further back here.' But the idea is we stick to it, keep the ball and build. What the manager says is: 'We're going to get so good at what we do, we're not going to compromise that, we're going to stick to our principles and just get better because the top sides, the really top teams who have mastered this way, are the ones that gets success.'"

Pressed on who he means, Baines continues: "I'm reluctant to say Barcelona or Bayern Munich, but it is based round those principles. We're trying to gain an advantage in what we do. It's attacking football, and we just have to trust ourselves." To clarify, none of this is intended as a slight on Moyes.

Baines, contemplating a fairly wretched season for the club he could have joined, actually sympathises with his old manager. "He's a fighter. He'll never give up on anything because it's not in his nature. And he has said he will get it right in the end. It's just that every time United have started to get a bit of wind in their sails, it's been taken away again. They needed to get a run going to lift their confidence and they have never quite managed it.

"A lot of the coaching staff went over there with him and it's tough seeing them all having a difficult time. But I also think they knew it was going to be tough. Maybe it's been tougher than even they expected. They knew they needed to strengthen and they couldn't quite do it."

We are talking after Baines has taken part in an Adidas shoot with Luis Suárez and David Silva – three stars of the Premier League in the unusual surroundings of Leigh, just outside Wigan – and it all seems a long way from the first time I met him, just after he had joined Everton, when he seemed almost in awe of his new club.

The younger Baines, by his own admission, could be filled with self-doubt, once admitting that he worried "every week about being found out" at Wigan, and that he dreaded going into Everton for his first day in case it turned out he was not good enough. Though he now says he "said some of those things because I didn't want people to think I'd got too far ahead of myself".

At Wigan, there were "three or four other lads who took the free-kicks or corners ahead of me and Jimmy Bullard in particular was very good at them". The pecking order changed in October 2006. "I was bullied into having a go really. It was against Man United, quite far out, and I don't think anybody wanted to take it and miss. So they turned to me and said: 'Go on, just whack it, put your foot through it.'" That one went in the top corner.

These days, Baines has the credentials to be recognised as the best striker of a dead-ball in the Premier League. Though it may surprise you to learn that he keeps practice to a minimum. "If you have 20 balls it can lead to bad practice," he explains. "It's much better to have three. Three one side of the goal, three the other, and you know that's all you've got. Just work on that. Focus. Imagine you're in a game situation. Put it in."

He is 29 now and talks like an experienced pro. "I can't ever take anything for granted," he says of his World Cup place. "Ashley is still a formidable guy to get past. He's almost robotic in terms of the level he's produced and stayed at. Just look at him in the last England game. He hadn't been playing for Chelsea and then he turned up, played great and looked as fit as anyone."

Baines has benefited from the way Cole has been shunted to the edges at Chelsea but still sounds surprised about the way it has panned out. "I think everyone's surprised. I don't see any reason for it."

There are generous words as well for Luke Shaw, the third candidate at left-back. "He looks a really good player and a good kid, too. He's got his head screwed on, focussed, not getting carried away. He's got all the attributes."

Yet Baines is mostly keen to make a point about another defender in Roy Hodgson's thinking: his Everton colleague Phil Jagielka. "People don't give him enough credit," he says. "He's really quick, for example, yet people don't seem to realise it. Maybe it's deceptive. But I've seen him so many times where we have been exposed on a counterattack, one-on-one, and I just know the attacker isn't going to get by him. He's quick. He's a leader. He sacrifices himself for the team. He's been amazing in the World Cup qualifying campaign."

These are good times at Goodison, even if the midweek defeat to Crystal Palace came as a jolt. If everything goes according to plan, they could be a Champions League club this summer, as well as providing two members of England's back four in Brazil. "I've felt throughout qualifying that I've been much more a part of it," Baines says of his England career, now up to 22 caps. "I've been playing more games and taking a more important role. It's all started from there, progressively getting into a stronger and better place, and it's nice to have that bit more self-assurance now."

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