Monday, 9am. Sincil Bank is shrouded in fog but the impact of the Cowley brothers and the FA Cup on Lincoln City is clear. Hundreds queue for tickets for Saturday’s fourth-round tie against Brighton & Hove Albion, the Championship leaders, even though, as season-ticket holders, they have until Wednesday to buy them. “The managers have had a huge impact,” says Nigel Godfrey. “The joke around the club is when do they ever sleep?” Godfrey got up at 4am to drive from Manchester and is heading straight home. “I’ve got to get back for the school run.” The Cowleys’s example of reward through sacrifice has resonated.

Supporters who stood in the bitter cold outside Lincoln’s home of 122 years, some from 4.20am, shared two common beliefs as club staff offered tea, coffee and £2 bacon rolls. A return to the Football League after a six-year absence remains the priority for the National League club despite illuminating the FA Cup third round with their defeat of Ipswich Town. Not since the late Graham Taylor in the mid-1970s has a manager had such a unifying effect on Lincoln the club and the city as Danny Cowley and his assistant, Nicky.

“The town is buzzing again,” says David Louth. “The manager has brought everybody together.” Marlene Beaumont, one of many who travelled to Barrow on Tuesday for a televised game and a surprise 3-0 defeat, says: “The fans stuck by the club through the bad times and now we’re getting the good.”

That loss at Barrow was Lincoln’s second in all competitions since 24 September – they have also advanced to the third round of the FA Trophy – and they remain top of the league by four points from Forest Green Rovers. Appreciation for the manager responsible is evident as he approaches the season-ticket holders, shaking hands, stopping for a chat or a selfie with anyone who asks. The feeling is mutual.

Cowley heads to a managers’ meeting while players have breakfast in the executive lounge where staff discuss catering requirements, toilet problems and making a good impression on the BBC when Football Focus and Five Live arrive on Saturday. The chef is enamoured at the thought of meeting Chris Waddle. Around them, the Soccer AM crew is preparing to film Jimmy Bullard’s “You know the drill” sequence later in the day. The city is buzzing, its club alive.

“From the moment I got here I felt it was a great club with lovely people,” says Cowley. “But the club had drifted since relegation. It hasn’t finished above 13th in this division and it felt like the club was in mourning. We have tried to give it some direction. It has taken me 38 years to become involved in full-time football so we have brought enthusiasm to the job. We love what we do and we have a very honest, hard-working group of boys.

“We felt some supporters were disillusioned and we wanted to bring everyone together. What I love about football at this level is the connection between the players, managers and supporters. That is the unique selling point. We can’t reproduce the quality of the football or the aesthetics of the Premier League but what we do have is the human connection and that is really important. We are all part of this.

“We took 5,000 to Ipswich. I’m a West Ham supporter and the West Ham away support can be pretty vociferous but I’ve never witnessed an atmosphere like that. Never. As a consequence of kind of being in the middle of nowhere there is a real allegiance to Lincoln City and that makes it really powerful. The passion of our supporters is unbelievable and it keeps you honest, focused and driven.”

Lincoln City fans queue to buy tickets for the FA Cup game at home to Brighton. Photograph: David Sillitoe/The Guardian

Parallels with Taylor – the last man to lead Lincoln into the FA Cup fourth round, in 1976 – are poignant following the former England manager’s death but Cowley was aware of his predecessor’s influence from the moment he arrived from Braintree Town last May. “We spoke to as many people as we could to get a real feel for the club and they all mentioned Graham Taylor and the 75-76 squad,” he says. Having finished third in the National League last season with part-time Braintree, following three promotions and three cups at Concord Rangers, Danny and Nicky left their jobs as PE teachers in Essex to go full-time with Lincoln.

We spoke to as many people as we could to get a real feel for the club and they all mentioned Graham Taylor Danny Cowley

“For us, it was never a gamble because we trusted our skill-set and we believed in our work ethic,” Danny says. “We knew we were going to work hard and neither of us want to live with regret. For Nicky and I, as regular people, these opportunities don’t come around, certainly not every day, so it was a straightforward decision.”

Their young families have stayed in Essex while the brothers immerse themselves in the goal of reaching the Football League. Grimsby Town and Notts County reportedly inquired after the Cowley brothers but Lincoln’s chairman, Bob Dorrian, said no and extended their contracts until 2021 on 12 January, the day Taylor passed away.

“They gave up a good pension and job security to come here full-time,” says Chris Ashton who, as referees and media liaison, volunteers to run the supporters’ travel club, among other tasks, and whose encyclopaedic knowledge of the Imps has prompted the affectionate moniker of Mr Lincoln City. One of those fans, in other words, who represents the lifeblood of a community club. “From the second we saw them it was clear they were something special. They are workaholics. I mentioned to Danny that if we beat Ipswich we’d have to go to Barrow in midweek. He said that was not a problem for a full-time manager because last season he was doing the same thing part-time with Braintree and going straight into school the next morning. He does 20-hour days. His analysis is unbelievable.”

Dick Tacey, Lincoln City’s kit man. Photograph: David Sillitoe/The Guardian

Ashton was taken to his first Lincoln game aged two years and nine months. His parents are still regulars, in the VIP lounge these days, and his father reckons he has missed 13 home games since the 1930s. Now 63, Ashton is well-placed to put this season into perspective. “This has had the biggest impact on the city and the club since the days of Graham Taylor. In terms of the community this is the biggest step forward for 40 years,” he says.

Monday, noon. It is still foggy, still cold, but the ticket queue has grown substantially by the time Cowley and his brother gather the squad for a video analysis session. There are reviews of the Ipswich replay and the defeat of Dover Athletic three days later before attention turns in meticulous detail to Barrow. Their opponents’ tendency to load the box at set pieces and a defender’s weakness on his back post are highlighted – and worked on in the training session that follows on the 3G pitch opposite the stadium – and there is further video analysis on the coach trip to Cumbria. It is therefore galling for Lincoln when Barrow take an early lead from a free-kick launched to their back post.

Things have changed since that goal. Me and the missus went out for dinner and I was recognised much more than before Nathan Arnold

Kevin Cooke, managing director and vice-chairman, calculates the FA Cup run has generated £500,000 for Lincoln who, having cleared a £380,000 debt to the Co-operative Bank in 2015 and upgraded facilities last summer, can use the money to “strengthen our squad for the rest of the season and into next season”.

Cooke adds: “We’ve had a lot of investment from Clive Nates, who has put in £400,000 over the last 12 months. He is a South Africa businessman but a lifelong Everton fan. We used to have a tie-up with Everton, which is how he heard of Lincoln. Walter Smith was manager at the time and I remember finalising the deal with the chairman, Sir Philip Carter, who said he may have to interrupt the meeting for a very important phone call. It was to say a headmaster had allowed a young boy to leave school early to sign for the club. Carter said: ‘We’ve just signed a boy called Wayne Rooney. You’ll be hearing a lot about him.’” A significant day for all parties.

Lincoln’s success is not only measured in terms of results and finances. For Nathan Arnold, scorer of that immaculate injury-time winner against Ipswich, there is wider recognition. “Things have changed since that goal, though – life has been different,” he says. “Me and the missus went out for dinner the other night and I was recognised much more than before. But it’s been nice for the people of Lincoln to have their football club doing well and to see them coming back in large numbers. We need to embrace it.”

Danny Cowley and Nicky, his assistant and brother, prepare Lincoln’s players. Photograph: David Sillitoe/The Guardian

For Paul Hamnett, chief executive of Imps in the Community, this season has “exploded interest” in a registered charity operating in an area where the council has closed its sports development department and cut its neighbourhood working budget by 98%. “We work with people who cannot access mainstream services, community groups, care homes, the probation service and the fostering service,” he says. “We are trying to reach the most vulnerable people who aren’t necessarily interested in Lincoln City but because of the lack of services due to government cuts, we want to fill the gaps. We can’t say yes to everything but we want to work with those who have the community at heart and the success of the football club helps get that message across.”

Cowley headed home to Essex from Barrow – 320 miles or so – and only then allowed thoughts to turn to the FA Cup prospects of one of two non-league teams left in the competition, the other being Sutton United. “We are not ahead of ourselves,” he says. “We did great over 180 minutes against Ipswich and I honestly think we deserved to come out on the right side. The levels we got to were a benchmark for us.

“Brighton are on a fantastic run and in a very confident place. It will be a huge challenge. We said Ipswich was like climbing a mountain so I suppose beating Brighton will be like getting to the moon.”

Monday, 4pm. The TV crews have gone, as have all the bacon rolls, but the fog and the fans who have waited almost three hours to buy an FA Cup ticket still linger.