Carl Jenkinson is being annoyingly sensible as he contemplates the improbable run of form that has lifted West Ham United from relegation candidates to Champions League contenders. It is nearly Christmas and West Ham are still fourth, their best start to a Premier League season. Their squad is easily the finest they have seen for years at Upton Park and it is natural to wonder if the transformation is permanent.

Jenkinson is optimistic but cautious. He says the right things, admitting that qualifying for Europe has to be the target but he resists the urge to make any bold claims. There is a desire at West Ham not to get carried away and that mindset will not change even if they win for the fourth time in five matches when Leicester City visit Upton Park on Saturday. The manager, Sam Allardyce, believes his side should not be judged until the end of January and Jenkinson’s view is similarly measured.

At which point it is revealed to him that Andy Carroll went off-message after he scored twice in the 3-1 win over Swansea City two weeks ago and said that West Ham can challenge for the title. Jenkinson has a good old chuckle about that. “I think he was getting a bit carried away there,” Jenkinson says. “Did he actually say that? Oh, brilliant! At least he’s optimistic. I think that one’s a bit far-fetched. Like I said, European football would be fantastic. That’s the goal and everyone’s just working hard to achieve that. But it’s not unrealistic.”

It is hard to argue with that assessment at the moment but West Ham’s rise has caught people by surprise. They are playing good football and their new-found sense of belief is typified by the way they fought back from a goal down in their past three matches. “A couple of lads have said to me that in previous seasons when they would go a goal behind they wouldn’t come back,” Jenkinson says. “That’s a real sign not just of the quality but also the spirit in the squad. Mentally you have to be on it to come back. You have to be prepared to keep playing and believe in your style of play and I think we did that against Swansea especially. It’s not easy in the Premier League to come back from behind.”

Facebook Twitter Pinterest Jenkinson challenges West Brom’s Saido Berahino during West Ham’s win at the Hawthorns earlier this month. Photograph: Matthew Lewis/Getty Images

Jenkinson’s role in West Ham’s revival should not be overlooked. Although he has been overshadowed by the attacking players in Allardyce’s squad, the right-back has been outstanding since joining on a season-long loan from Arsenal, the 22-year-old’s speed and energy giving West Ham far more impetus going forward.

West Ham’s diamond formation has not only brought out the best in Stewart Downing but also given their full-backs more responsibility. Jenkinson, who supplied the cross for Carroll’s first goal against Swansea, and Aaron Cresswell have both caught the eye.

“As a full-back you always have to focus on your defensive job but the modern-day full-back has to get forward and you have to get back if the attack breaks down,” Jenkinson says. “It’s not an easy job any more. I think you used to just be able to stay in your own half and it used to be more straightforward but it’s not like that any more. But I enjoy that, I like getting forward and getting crosses in. It’s fun, you want to be involved in the goals. We’ve got the lads in the box who can head the ball like not many others in the league can.”

Jenkinson’s family history helps his style of play. His father, Steve, ran the 800m at a high standard and trained with Sebastian Coe. “I have that in my genes,” Jenkinson says. “I used to run for the school and the district. I used to love running. I treated it as a way of getting fit for pre-season. I would go to my local running club, Woodford Green. I used to love athletics and always did the cross countries. It sort of went hand in hand with football actually, because it was a sport you could do. I was playing at an academy so I couldn’t be playing rugby, but it’s hard to get injured running. If anything, it’s a good thing.

“I was good at the cross country, I had good endurance. I was decent at the 100m when I was younger. I don’t think I ever really got beaten until Year 10 and 11 and then I was pushed down the pecking order a little bit. It was more 400m. If I was running now, it would probably be 400m.”

He is unsure what his 100m time would be now. “I could say something wrong here and then all of a sudden people think I think I’m Usain Bolt,” Jenkinson says.

Jenkinson’s dad also gave him a love of Arsenal. He was a Junior Gunner, his favourite player was Tony Adams, Lee Dixon was an inspiration and his most cherished memories are of watching The Invincibles.

His life revolves around football but it is important for Jenkinson to find ways to relax in his spare time. “I do a bit of fishing,” he says. “I go with Mark Noble a lot. A lot of the things I do are decided around football and fishing is the perfect hobby as a footballer because you just rest and relax. You can do other things but a lot have you exerting energy, if you’re playing golf, say. Whereas fishing you go and chuck your rods in and you’re sitting down having a chat for hours.

“It’s good for your mind as well because you can just switch off. There’s not many things you can do where it’s like that. Normally we just do a night and we’ll go in the afternoon after training and stay for the night, put our tents up. He’s better than me, to be honest. He’s a more experienced fisherman. The geezer’s got a souped-up fisherman’s van. He’s got a van which is all insulated and he sleeps in that. I’m sleeping in a tent by the lake freezing cold.”

Facebook Twitter Pinterest Jenkinson says it was important for him to leave Arsenal and start playing regular football. Photograph: Richard Heathcote/Getty Images

Jenkinson is learning plenty of new things at West Ham then and he feels he has improved under Allardyce. “He’s been absolutely brilliant,” Jenkinson says. “I didn’t want to go on loan to a team that was just going to kick the ball long. I wanted to go to a team where I was going to learn and improve and I think I’m definitely doing that here at West Ham. We focus on defending in training and we do a lot of work on one-v-ones and heading and I feel I’ve developed in those areas. He’s given me the licence to get forward and express myself. I know what I’m capable of.”

Jenkinson is unrecognisable from the naive teenager who was thrown in at the deep end after joining Arsenal from Charlton Athletic in 2011. His fourth game was against Manchester United at Old Trafford but Arsenal lost 8-2 and Jenkinson was sent off. It took strength of character to recover from such a torrid experience; he won his first and only England cap a year later.

In an ideal world he would not have gone on loan but the writing was on the wall when Arsenal signed Mathieu Debuchy. “I didn’t want to have another season sitting on the bench,” Jenkinson says. “It was starting to drive me up the wall a little bit, I wanted to get out and play football, and I’ve realised that I’m happiest when I’m playing regular football.”

And West Ham were a good fit. Growing up in Essex, he always had a soft spot for them. “I have a couple of friends who are West Ham and they’re absolutely buzzing,” Jenkinson says. “I’ve got a feel of what it means to everyone at the moment and how good it is for everyone involved at West Ham with where we are in the league. That gives you motivation to keep it going and keep achieving. It’s nice to see other people enjoying your success.”