I'm not sure the class war is greater. I think it's been maintained for some time. Rugby League's big issue in England is that it never won the PR war against RU.
In Australia, RL went after RU and proudly boasted how fair it was. It helped too that strong Workers Union men and the sports darlings Dally Messenger and Victor Trumper were with the new code.
RU in the UK managed to make it a matter of religion as well as class, which helped them to not only show that professionalism was detrimental to the sport, that it was also inherently evil. (The religious angle was revisited by the Vichy Govt during WWII to justify their decision to delete RL).
RU was hit so hard and so savagely in 24 months in Australia, by the time they got their shit together, RL had reached it's third year, poached Messenger and 80% of the Wallabies, while also getting the game introduced in Sydney's Catholic Schools. RU was on the back foot and all they could do was stage public battles about which code was morally acceptable.
After WWI ended, RU was the second Rugby code in Australia and they never recovered.