Arsenal’s victory at Liverpool may go some way to reassuring restive fans that this campaign will not be a repeat of last season. Then, after suffering their worst start in nearly 60 years, Arsenal just edged Tottenham in the race for the Champions League, largely due to the collapse of their bitter north London rivals.

But, even before Sunday’s success, Arsenal chairman Peter Hill-Wood had no doubt that wider horizons beckon this season. We met at his home in Sandwich as the Old Etonian prepared for his annual holiday to Long Island in New York and the 76-year-old could not have been more confident.

“We have a pretty good chance of challenging for the Premiership,” he said. “I don’t see why we cannot win it this year.”

The bookmakers do not share Hill-Wood’s confidence. Sunday’s win shortened the odds from 25-1 to 12-1 but Arsenal have not won the title since 2004, or any trophy for seven years.

Their chances were hardly enhanced by the sale to Manchester United of leading scorer Robin van Persie, double footballer of the year, golden boot winner and scorer of his first hat-trick for his new club on Sunday. Despite this, and Theo Walcott refusing to accept a new contract, Hill-Wood came across as a man with no fears.

“It is not a worry to the board that we haven’t won a trophy since 2005,” he said. “It would be lovely to win but it’s not that easy. Liverpool haven’t won the title for 20-odd years. We’re very ambitious and want to win but, if you don’t have billions of petro-dollars to throw around, you’re going to have to do it some other way. That’s what we’re trying to do — with skilful selection of players. As for Walcott, he did not accept our offer so nothing is happening.”

Fans expected the club to do more in the close season with some £60million available to manager Arsene Wenger. But the transfer window saw Arsenal make a profit on their dealings and Hill-Wood insisted: “Arsene has money to spend but there’s a limit. We can’t spend £50m on one player.

“At a certain level, we can’t compete. I don’t think Stan Kroenke [the American owner] is going to put the sort of dollars in that [Roman] Abramovich or Sheikh Mansour are putting into Chelsea or Manchester City. That’s not the way he thinks clubs should be run.

“Luckily, Arsene understands that. He got an economics degree from Strasbourg University so he’s certainly no fool. He knows how a club should be run. That annoys a lot of people but clubs have to be sustainable. We’re not going to go bankrupt in the way one or two other well known clubs have.

“The Glasgow Rangers example is something we’ve all got to guard against. They spent far more money than they could afford. We’re ambitious enough but we’re not going to end in the same plight as Rangers. That is a fact of life. So my advice is don’t get miserable about it.”

Not all fans are willing to accept that advice and, last season, at many home games, some 5,000 did not turn up despite having paid for their tickets. Given the cheapest season ticket cost £1,000, that was some statement. And, for the first time Emirates heard the chant, ‘You don’t know what you’re doing’.

Hill-Wood could not hide his contempt for such behaviour: “What those fans shouted did not influence me one little bit. I was disgusted to hear them because Arsene’s been absolutely outstanding. He is still outstanding.”

The summer brought talk of Wenger managing France but Hill-Wood saw no reason why his manager should leave.

“You occasionally hear rumours of him going somewhere. I do not think that is likely to happen. He’s very happy where he is. He has a very good job in that we don’t interfere with him. We agree with most of the things he says and he agrees with most of the things we say. I have seen some really successful Arsenal managers but Arsene has revolutionised the club.

“I would say he has been a bigger influence than Alex Ferguson on Manchester United in the way he has changed the traditions of the club and the outlook of the Premiership.”

Arsenal fans would argue that Wenger has not been the same man since his good friend David Dein was sacked as vice-chairman in 2007 but Hill-Wood refused to accept that. “I don’t think David Dein’s departure has impacted on Arsene at all,” he said. “Arsene has a very good relationship with Ivan [Gazidis, the chief executive reportedly on £2m a year] and it’s very businesslike. He and Arsene get on very well.”

And, unlike Ferguson, who has regularly refreshed his backroom team since his arrival in 1986, Wenger has worked with the staff he inherited, apart from coach Boro Primorac who came with him. Normally managers come with their own team but, recalled Hill-Wood: “I asked Arsene whether he wanted to do that and he said, ‘No thank you, I’m very happy’.

“He’s appointed [youth-team coach] Steve Bould to succeed Pat [Rice, who he inherited as assistant manager]. I very much agree with that. To me, it reflects Arsene’s confidence.”

Hill-Wood’s own confidence in Arsenal’s future may stem from the fact that the club have long solved their ground problems with the move from Highbury to Emirates Stadium. This is in sharp contrast with many of their London rivals — Chelsea, West Ham, QPR and particularly Tottenham — all struggling to find new homes.

He saw this as a hindrance for their neighbours. “I do not see Spurs posing a problem for us this season,” he said. “Their new manager [Andre Villas-Boas] may be a great success but they have to find a stadium. That’s going to be very difficult. Finding a site and financing it is a major problem which we know all about.”

Now that Emirates has proved a success, Hill-Wood happily confessed: “I was very nervous and didn’t see how the hell we could finance a new stadium. It’s worked out very well.

“Quite a lot of equity went into it and payments from Nike and Emirates helped enormously. We’ve got a stadium debt of around £230m now, which is a 25-year bond at a fixed rate of 5.5 per cent.

“The success of the stadium is due to Danny Fiszman [the deceased director] and Ken Friar [a long-term director], who did a spectacular job. Danny was a genius and I don’t think we’d have achieved what we have without him.”

The stadium development was driven through despite the opposition of Dein, who wanted Arsenal to share Wembley, an option that appalled Hill-Wood.

“It would’ve been crazy to have gone to Wembley,” he said. “I hate Wembley anyway. It’s a bloody long way away. And I would absolutely not have wanted to be a tenant of the Football Association.”

He was just as implacably opposed to having Alisher Usmanov, who owns 29.9 per cent of Arsenal, on the board. The Uzbeck billionaire has questioned the ambitions of the club and the board members’ ability to ensure Arsenal can again challenge for the top table.

Usmanov cleverly timed his four-page open letter to the board to arrive the day after Van Persie made it clear he would not sign a new contract. The letter raised questions about the board, whose average age is around 73, and many of whom have made millions selling their shares to Kroenke.

Although Hill-Wood once said investing in football was “dead money” the last lot of shares he sold yielded £5.5m. He explained the gains by saying, “You wouldn’t say no to it,” and of Usmanov’s letter, he told me: “He’s said that before. It was nothing new and I didn’t think it was particularly relevant.”

As for Usmanov getting on the board, Hill-Wood added: “It’s not entirely in my hands. I don’t think Stan Kroenke wants anybody else on the board. I have met Usmanov but I don’t think he would fit in, that’s all.”

Some Arsenal watchers speculate that the hierarchy fear that Usmanov’s presence on the board could see the return of Dein. “No,” said Hill-Wood and, while he gave no further explanation, his tone appeared to suggest that Dein is now a pariah at the Emirates.

Hill-Wood, who joined the board in 1962 and succeeded his father as chairman 20 years later, has no plans to retire. “I’m going to carry on until I get completely senile and then my colleagues will say, ‘It’s time you went’. But, at the moment, they haven’t got to that stage. I’m not indicating that I’m complacent but, generally speaking, the club are on a very sure footing and the potential is there.”

The Liverpool result has further fortified this optimism but, for many fans, the jury will remain out until Wenger regains his trophy touch.

Follow Mihir on Twitter @mihirbose