McLaren are an unfamiliar sixth in Formula One's constructors' championship, trailing Shara Force India by 10 points. There are fears this could be the first year since 1980 that they fail to win even a podium place. Margaret Thatcher was prime minister then and Bjorn Borg won Wimbledon for the last time, beating John McEnroe in the final. "That's the year I was born," says Button.
McLaren, though, have won six of the last eight races at the Hungaroring and Button adds: "This is our best chance of a podium but it does not mean we will be getting a podium.
"Over history here McLaren have done very well. I have also won two races here. I like the circuit and the layout. It is physically challenging and mentally challenging. With the temperatures this high it is going to be tough for everyone.
"Because it is going to be so challenging, plus the unknown factor of the tyres, it's going to be our best opportunity to get a good result.
"But I don't think we are going to get a podium here. We have to be realistic. A good result would be good for going into the summer break."
Button, whose best finish this season was his fifth in China back in April, says he would trade isolated glory for being competitive in the world championship. "For me it's not important to get one win in a season. I would rather fight for the world championship.
"But for the whole team it would be great to win a GP and we are going in the right direction to do that and it has to be the goal. We won't settle for anything else.
"The mood is good and positive. We were not happy finishing sixth in Germany but it was a good step over the weekend and, if we can have something like that, but a bit better, then it will help morale around the factory, which is pretty good anyway."
McLaren have already said that their main focus now is on next season. "We are concentrating more on 2014 but we are putting bits on this car which will help us for next year. It is not as though we are finishing with this car. With people wanting to see a result, it is wrong just to focus on next year. So there will be new things for this car which will help us with the design of next year's car."
Button's ninth place in Friday afternoon's practice session did not inspire much confidence in him winning that elusive podium place; his team-mate, Sergio Pérez, was 12th. Button had been a more successful sixth in the morning run, with Pérez ninth.
Both morning and afternoon sessions were won by Sebastian Vettel, with his Red Bull team-mate, Mark Webber, second.
Webber narrowed the gap in the afternoon but it will be a surprise if Vettel has not increased his lead in the championship by Sunday evening.
Lewis Hamilton, three times a winner at the Hungaroring with McLaren, was 13th in the morning but improved to sixth in the afternoon. Vettel could end the recent dominance of Mercedes in qualifying on Saturday afternoon.
Vettel said: "It's nice when you feel in control of the car and you can play around. I think the car suits the track. First practice and second practice were very good for us, which I think is a bit of a surprise. I think tomorrow will be closer and we have to make sure we get everything out of the car."
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image: © Paul Williams