Even just looking at Victorian Britain there is a huge class division across sports, across borders, and even within the same sports. It's not quite as simple to say that certain sports were for the lower classes, middle classes and landed gentry.

For this I will be looking at the role of class within two British sports, rugby and Cricket, and the different relationships different classes had with the them.

Taking rugby first, it is a game that was born out of the public schools of England. Although games like Rugby Football had existed within Britain for hundreds of years, the formation of the a rugby league was the direct result of the popularity of the Rugby School style of football. In England, rugby union was a game that was spread through the public school system and consequently through universities. This meant that from the very beginning of the sport, the audience and the players were from the middle and upper classes, a trait that continues through to this day, at least in England.

Rugby arrived in Wales in 1850 although, like England, similar games had been played since the middle ages with the Celtic game of cnapan. Wales first received rugby through a Cambridge graduate, Reverend Professor Rowland Williams. Unlike in England, however, where rugby was a game spread through public schools, Welsh rugby grew from the industrial heartlands of Newport, Cardiff and Swansea and spread out from there as other industrial centres developed and workers moved around the country via the railways. This is also why a number of the most successful Welsh teams were based in areas of extremely heavy industry, either iron or mining.

The rivalry between Wales and England has often been seen one based as much on classism than of history. In the 1977, Wales captain Phil Bennett said in a prematch speech:

Look what these bastards have done to Wales. They've taken our coal, our water, our steel. They buy our homes and live in them for a fortnight every year. What have they given us? Absolutely nothing. We've been exploited, raped, controlled and punished by the English — and that's who you are playing this afternoon.

Rugby is the ultimate sporting example of the relationship between sport and class between different countries in Victorian Britain, in my opinion.

But the differences are more than country to country, and there are examples of a tight, inbuilt class system within the same sport within the same country.

Late Victorian cricket had something of a problem. The problem had seen the standard of cricket continually tumbling and, despite there being an abundance of talented players who could play the game, a decline in the numbers of quality players actually playing cricket.

The cause was the inherit classism within the cricketing world of the time. Although cricket still now has an air of toffery and the whiff of overt traditionalism, the problem has never been as bad as it was during this period. The British cricketing world was split between the Amateurs and the professionals.

The Amateurs were almost always members of the landed gentry who could afford to play cricket full-time without the need for payment, being able instead to live off their vast inheritances or the regular money that was coming in from their lands. The professionals were the complete opposite; members of the lower classes who made their living playing cricket. Not huge sums, but they had no inheritance to rely on, no land to live off. They were mostly from working class families, born and brought up in houses near to a town cricket pitch. This was during the era of cricket booming in popularity amongst the working classes and cricket pitches today are very often located in amongst tight terraced houses in industrial parts of cities.

The professionals were, to put it simply, a lot better than the amateurs. There was an expectation that you had to be good enough at cricket to become a professional, whereas the amateurs just had to be able to afford it - a lot like drama schools today. However, the ECB [English Cricket Board] championed amatuer cricket as something honourable and although they would pick professional players for the England Cricket team, they wanted the amateur game to be perceived as superior. This caused a great problem as the professionals weren't just better, it was embarrassing. When batting the professionals had to have an extra stump to make it easier for the Amateurs to bowl and amateurs would often turn up to matches drunk.

An old, definitely apocryphal story goes:

two cricketers - one an amateur, the other a professional - were talking about batting. "Do you have trouble with a particular number?" asked the amateur. "How do you mean?" replied the professional. "Well," said the amateur, "I always seem to get out on one or 11." The professional: "Oh, I see what you mean. Yes, I do, as it happens. I never seem to get past 189."

Worse still, the amateurs were riddled with the trappings of the upper classes: often refusing to travel North to play matches, never playing after the 'Glorious Twelfth' (the start of grouse hunting season in August), and when they were playing on the same team they were often indescribably rude, insisting that the professional team didn't even come through the same pavilion doors to enter the ground at the start of play. When touring together the amateur were amazed that the professionals wouldn't ride in first class trains together, attributing this bizarre notion to "not wanting to change for dinner."

To be blunt, class and sport are so tightly intertwined in Victorian society that it's less a question of deciding what sports were purely upper class and working class, but trying to find the distinctions within each sport itself. And if you really want to see more how class can impact a sport, just like cricket, English rugby has a huge class divide that actually saw the sport split in two, with the Northern, working class teams breaking away to for the Rugby League, and southern teams collating to form the union. The class rift between them still exists to this day.

I hope that my answer, although at times rambling and slightly veering off from the original question, has been useful to you.

Sources

Smith, David; Williams, Gareth (1980). Fields of Praise: The Official History of The Welsh Rugby Union. Cardiff: University of Wales Press, Cardiff

Richards, Huw (2007). A Game for Hooligans: The History of Rugby Union. Mainstream Publishing, Edinburgh

Best, Geoffrey (1971). Mid-Victorian Britain, 1851-75. Flamingo Press, London

Collins, Tony (2009). A Social History of English Rugby Union. Routledge, London

Grace, W.G (1891). Cricket. J. W. Arrowsmith. Bristol

Steel, Mark. The Mark Steel Lecture: W.G. Grace. BBC Radio 4, London. Broadcast September 1999.

Shindler, Colin (2012). The Slow death of Cricket's class divide. John Wisden & Co. https://www.espncricinfo.com/wisdenalmanack/content/story/573224.html