When you think of boxing, bloody noses and broken teeth probably come to mind first. But boxing as a glorious tradition of racial integration? Yet for over 200 years now, boxing has been an engine of social change, helping newcomers to Britain to make a mark of their own, as this new exhibition shows.

The Jewish Museum, set off a leafy street in Camden Town, north London, seems an unlikely place for a tale of muscled men beating the hell out of each other. It’s all so civilised and quiet, a world away from the bruising history which the exhibition Ghetto Warriors evokes. Not solely concerned with Jews who have been boxers, but all migrant communities into Britain, Ghetto Warriors follows the trail from pre-Victorian bouts to the recent Olympic success of Amir Khan.

In the eighteenth century, well before the Marquess of Queensbury gave his name to the rules which revolutionised boxing, and gloves became required kit, not optional extras – we can see members of ethnic minorities slugging it out for glory and respect. Daniel Mendoza was not the first Jewish boxer, but he was the first to gain national attention and surely the first to teach the upper classes how to punch each other. An engraving by celebrated artist James Gillray from 1790 shows him tensed for the fight in front of a crowd of hundreds, his fists at the ready.

Mendoza did not have to go far for his success, having been born in Aldgate, east London. Bill Richmond and Thomas Molineaux certainly did. Richmond, the son of ex-slaves, was invited to England from New York by the Duke of Northumberland (again showing the aristocracy’s fascination with the sport), while Molineaux came over from Virginia. 15,000 people watched Molineaux fight England’s champion Tom Cribb in 1811. Molineaux’s fame was guaranteed despite his loss, and an engraving of the fight is on display.

The stories of Mendoza, Richmond and Molineaux have several similarities, which run through the lives of later boxers from immigrant communities: not only a desire to get out of impoverished circumstances, but a need to defend themselves from attacks and taunts. The racism of the native population drove many people to their fists for their own safety, making boxing not initially about glory but survival.

Despite boxing potentially bringing money and respect to immigrant communities, the sport sometimes seemed to be as much about suppressing ethnic identity as celebrating it. As soon as a Jewish boxer became a success – even in the twentieth century – he had to change his name.

Ted ‘Kid’ Lewis was one of Britain’s greatest welterweight fighters, winning a world boxing title in American in 1915 and the British Empire title in 1920, but he was born Gershon Mendeloff in east London. Johnny Brown and his brother Young Johnny Brown were born (respectively) Philip and Jacob Heckman. Clearly to be acceptable to a British audience, any overt racial difference had to be wiped out. This was obviously not possible with boxers of African origin, so English racism still had victims.

But there are greater subtleties to be picked up from the exhibition. Several pairs of boxing shorts from various fighters are on show, and both Ted Lewis and Young Johnny Brown have Stars of David on theirs. Young Johnny Brown in fact has his initials woven about the Star too, so he is clearly not ashamed of his religion. It seems to come down to a balancing act: people might never come to see a boxer with a Jewish name, but they could tolerate a symbol. This paints a revealing picture of these audiences.

As well as shorts, there are plenty of other boxing relics. Ted Lewis’ gum shield is in a cabinet, while Young Johnny Brown’s black leather gloves and soft boots still look like they could go a few rounds. Johnny Brown (the elder) won the Lonsdale belt, boxing’s supreme achievement (you must not only win it but defend it three times to keep it). His is on show, and it is much grander than the tacky contraptions given out to world champions today: thick gold chains run along a wide red, white and blue ribbon; porcelain medallions are spaced along the chains, painted with boxing scenes. It is elaborate and beautiful.

The exhibition ends with recent history and the photos of stars like Lennox Lewis, Barry McGuigan and Amir Khan. You can thus follow portraits of ethnic minority boxers all around the room. This stresses what has remained the same: boxing’s power to give fame and dignity. All the fighters we see won prizes, and that we can still see them shows how long their fame has endured.

But this sequence of portraits also reveals what has changed: society’s tolerance. Where once a boxer’s racial identity would be a subject of deep interest, now it is barely even thought about, or at most is taken as a sign of Britain’s success in integrating its newest citizens. It looks like the earliest boxers have won their fight for acceptance.