It is well known that Liverpool’s ground was once home to Everton, but in 1971 United fans called the Kop their home end

On Friday 20 August 1971 a team wearing red walked out at Anfield to rapturous applause from supporters bedecked in red and white scarves and standing on the Spion Kop. Their opponents were Arsenal, who had beaten Bill Shankly's side 2-1 in the FA Cup final to secure the double in May of the same year. But the home side were not Liverpool. They were Manchester United.

Hidden deep within the pages of football's dustiest history books lurks a dark secret – or so it appears. The club that now boasts 18 league titles, the same number as Liverpool, could once call Anfield its home, just as Liverpool's great city rivals Everton did in the 1880s. In 1971, with United banned from playing their first two home matches in Manchester, after hooligans had thrown knives into the away section at a match at the end of the previous season, their opening "home" games would be played at Anfield and Stoke's Victoria Ground.

But so forgotten is this forgotten story that even some Manchester United players who took part in the 3-1 victory over Arsenal cannot remember doing so.

A lethargic first-half performance by a United side still trying to find its feet under a new manager, Frank O'Farrell, following Matt Busby's departure in June 1971, found themselves trailing to a fourth-minute Frank McLintock strike. United would enjoy a stirring comeback in the second half thanks to George Best's growing influence, which led to an equaliser deftly lifted over Arsenal's goalkeeper, Bob Wilson, by Alan Gowling. A United goal at Anfield celebrated by the home fans must be among the rarest things in football. So such a memorable occasion would be dear to Gowling, wouldn't it?

"I can't remember," he says. "Who did we play?" I remind him that it was Arsenal. "United played a home match at Anfield? Give over," he says, incredulous. So inconceivable does it seem that one can almost understand Gowling's reaction, but a picture in the Guardian of 21 August, 1971 clearly shows him leaping over Wilson to celebrate his goal, scored at the Anfield Road End.

Would David Sadler, who commanded United's defence, recall the occasion?

"Was I playing?" he says. "I just can't remember. Alex [Stepney, the Manchester United goalkeeper] might recall it. He's better at remembering matches than me."

Stepney tipped a shot from the diminutive Arsenal winger George Armstrong against the bar at the Kop end in the second half to keep United in the game at 1-1. Did he enjoy being the only Manchester United goalkeeper in history to feel the full support of United's fans emanating from the Kop?

"I vaguely remember that we had to play two games away from Old Trafford, but I can't recall that match," says Stepney, who made over 400 appearances for United. Perhaps there's some kind of conspiracy to hide the truth.

"I thought I'd only ever won one match at Anfield, when we beat Liverpool 4-1 [in December 1969] – so I can add a second win now," he says. "The only one I remember playing away from home was when we played a home match at Plymouth [Uefa banned United from playing their home leg of a Cup Winners' Cup match against St Etienne within 200km of Manchester, following crowd trouble during a 1-1 draw in France in 1977]."

The Manchester United captain, Bobby Charlton, scored his team's second goal at the Anfield Road End with a free-kick curled around the wall and into the left-hand corner of the net. Brian Kidd, who is now Manchester City's assistant manager, wrapped things up with a goal in the dying minutes.

One man who can just about recall the match is the "Voice of Anfield", George Sephton, Liverpool's stadium announcer who had started the job a week before. "I can still see the half-empty ground," he says. "It was spooky. I had just started, it was an extra match, it was Friday night so a bit of peace and quiet, I thought."

And what of Liverpool's famous anthem? Surely United's players didn't run out as the home team at Anfield to "You'll Never Walk Alone"?

"It was only the third game in my career," says Sephton. "I couldn't swear on the bible but I'm almost certain I didn't play 'You'll Never Walk Alone' at the game. It's been 'our' song since 1963! It was weird because Anfield felt like a neutral ground but from my perspective I was just happy that I had an extra couple of quid in my pocket because I was young, just married and was saving up for a house.

"I don't remember any trouble on the night. The enmity with United wasn't as bad in those days as it is now so it was nice to turn up and watch a game which you weren't bothered about in terms of the result. If it happened nowadays of course, I'd be cheering Arsenal on. But now they would just play the match behind closed doors."

The FA's decision to send United to play at Anfield in the wake of a hooliganism incident seems hare-brained now, but at the time hooliganism happened at most games and in any case, as the former Liverpool club secretary Peter Robinson, who helped organise the fixture, explained last year, the animosity didn't exist as it does today.

"When I started at Liverpool in the 1960s the great rivals were always Everton," said Robinson. "The rivalry has changed. It turned into Manchester United when they had this terrific emergence but before that I can remember them being relegated [in 1974] and having some really difficult times. I can also remember United supporters standing in the Kop. It wouldn't happen today, would it?"

The rivalry between groups of hooligans was still fierce however, even if the antipathy felt between real football supporters of both sides was not, and the front page of the Guardian the morning after the match carried the usual depressing news of trouble. "About 100 fans" were ejected from Anfield, according to the report, the windows of some houses in Anfield were smashed and "600 skinheads" were said to have been "kept in check" by police after throwing bricks at the United supporters as they were frogmarched back to Lime Street station and on to trains back to Manchester.

The Guardian correspondent Eric Todd's match report brimmed with frustration at the behaviour of the fans in the Kop and of the wider trouble that was prevalent in football in the 1970s.

"Once again, certain sections of the crowd, whatever their places of origin were the villains of the piece," he wrote. "And those psychiatrists, amateur or professional who spend many hours trying to explore the minds – the word is used quite loosely of course – of certain members of the footballing public would have enjoyed last night.

"As soon as the teams arrived on the field the Kop vomited scores of young 'supporters' of both sexes who ran down the field to the end where United were warming up. The police, although hopelessly outnumbered, did their best and removed as many as they could capture. When the invaders discovered that United would attack the Kop end they retraced their steps and suffered further losses."

United would suffer further losses too. Liverpool were given 15% of the gate receipts from the 27,649 fans who attended the game and United were instructed by the FA to pay Arsenal compensation, as the gate was below the 48,000 that attended the fixture at Old Trafford the previous year. (Until the 1980s, gate receipts for league games were shared). Even Everton stood to benefit if the crowd at Goodison Park was below 46,000 the next day, for their match against Sheffield United.

You can stop whispering now. The secret is out.