British Transport Police said the worst brawl was on the 23:11 TransPeninne service when fighting broke out between two women and rugby fans at Carnforth Station on 10 October.
A spokesman said a "hardline" clampdown was needed to curb the problem.
Those considered too drunk would not be allowed to travel, he added.
Extra police officers will be patrolling the Lancaster to Barrow late-night weekend service after an increase in drunken behaviour.