Rail authorities say they will be stepping up their efforts to stop thefts after thousands of passengers were delayed on Friday.
A reduced service had to run for most of the day after copper wire was stolen from a signal point on the network near Tilehurst in Berkshire.
The delays affected services between Reading, Oxford, Swindon and London.
Network Rail condemned the "mindless" act and has vowed to fight the problem with British Transport Police.
A spokesman for BTP said: "It is a significant problems on the railways.
"We are doing as much as we can to address it."