Sam Allardyce is determined to revel in West Ham's best start to a season in almost 30 years.

Andy Carroll and Stewart Downing were on target in a 2-0 win over Leicester which means the Hammers are fourth in the Barclays Premier League at Christmas.

It is their highest position on December 25 since the 1985-86 season when they finished third.

Questions are bound to be asked if the Hammers can last the distance on this occasion, but with Chelsea and Arsenal the next opposition Allardyce is not looking too far ahead.

"It's not often a team are breaking the barriers everybody else doesn't expect them to break," Allardyce said.

"You should enjoy the moment and continue to enjoy the moment for as long as it lasts. Hopefully it will last for a good while yet.

"We've sustained our position between sixth and fourth in recent weeks. We've a considerable amount of games now. The end of January will tell us what we can possibly achieve.

"It's about the consistency of winning and that is what we've got to challenge ourselves to try to do. You can't afford to slip up too many times if you've played well and you don't win, because you'll end up slipping away and out of the elite end of this league.

"At the moment we're living with it, we're enjoying it and the players who have applied themselves magnificently well all season are reaping the rewards."

Leicester, whose winless run was extended to 12 games, were culpable as West Ham claimed a fourth win in five games.

Paul Konchesky, Barking born and playing against his old club, presented Carroll with the opening goal moments after the Hammers striker had missed a straightforward opportunity.

But there was little Leicester could do to stop Downing's strike, as the playmaker curled a sumptuous shot into the far corner.

Adrian saved well to deny substitutes David Nugent and Leonardo Ulloa late on as West Ham kept a cleansheet in a comfortable win.

The only negative for Allardyce was James Tomkins' departure, as a precaution, due to a hamstring problem.

"We've had a very good day," Allardyce added.

"Everybody expected us to win. We have won. That gives us a little bit of leeway for the next two coming up."

On the goals, Allardyce said: "A very composed finish from Andy on a one-on-one. He missed an easier chance before that.

"The whole team is playing really well, but Stewart crowned off a very good performance again with another goal. His outstanding contributions on a consistent basis have been a revelation for us this season."

While West Ham are on a high, Leicester are bottom.

Only twice before – West Brom in 2004-2005 and Sunderland last season – have the side at the foot of the Premier League standings on Christmas Day avoided relegation.

Leicester boss Nigel Pearson rued his side's failures in both attack and defence.

"Individual mistakes have been costly for us, but you've got to score enough goals and we've just not been doing that," Pearson said.

Pearson was fined B£10,000 and given a one-match touchline ban following his altercation with a fan during last month's loss to Liverpool.

But Pearson, who often watches from the stand, was on the touchline at Upton Park as he awaits the written reasons for his punishment from the Football Association.

The supporters sang about the Foxes boss early in the contest.

"It's not a story about me," said Pearson, whose side host Tottenham on Boxing Day.

"What is important is that the fans stay behind the club and the players."

Pearson has experience of a great escape, having been assistant boss to Bryan Robson at West Brom when they survived on the final day.

"It really is about us making things happen ourselves," Pearson added.

"I look around the dressing room and we've certainly got nobody who's giving up any sort of a fight.

"We're a side experiencing the polar opposite of what we experienced last year and that in itself is difficult. Get back to work and find the answers."