There are now as many as eight cases of attempted cable theft from the railways a day, operator Network Rail has said.
Dyan Crowther, the body's operations director, said the crime was spreading across the UK and had cost the firm more than £40m over the past two years.
Most cases were "random", she told MPs, and there was evidence thieves were impersonating engineering staff.
A senior police officer said it was seen as a "low risk, high return" crime and penalties were not tough enough.
Ministers have said they are looking at new measures to combat the problem and are being urged to give police greater powers and to tighten regulation of scrap metal dealers.
Ms Crowther told the Transport Select Committee that the problem of cable theft had first surfaced in the north-east of England about two years ago and had "migrated" steadily across the country.
While many cases took place at night, thefts were now regularly happening in peak time, she told MPs, and while there were "hotspots" there was no real pattern to their occurrence.
"It is quite difficult to predict and makes a response very difficult," she said.
There were now between six and eight attempted thefts a day, she said, which had cost Network Rail £43m over the past two years in terms of compensation paid to train firms and repair costs.
"It is a risk. It is a risk to our network daily and we are working very hard to mitigate those risks."
In the most high-profile case yet, in June cable thieves disabled the signalling system near Woking in Surrey, causing massive disruption for around 80,000 passengers in the evening rush hour.
Ms Crowther said drivers were being briefed to report "suspicious activity" on the network amid evidence that thieves were pretending to be engineering staff in order to gain access to the railway.
Measures being used to combat cable theft, she told MPs, included increased use of surveillance, reinforcing railway sleepers and spraying tracks with traceable liquid to deter thieves.
Also giving evidence, the British Transport Police said it had 110 officers working full time on the problem as it was aware it was having a "very significant" effect on communities and businesses.
"We take it very, very seriously indeed. It fills up much of our waking time," Paul Crowther, the force's deputy director told the MPs.
There was a "clear correlation" between price of copper on commodity markets and rates of crime, he told MPs, suggesting cable theft was largely the work of "professional criminals".
"All routes lead us back to the market," he said. "It is a very market-driven crime. It is almost as if the criminals are looking at the market themselves."
Legislation for dealing with the crime, dating back to 1964, was "outdated" and needed redrafting.
Those selling scrap metal to dealers did not have to provide proof of their identity and, unless this was tightened, it would be "almost impossible" to charge someone if the material was obtained illegally.
"It really is Steptoe and Son legislation which has not kept pace with current methods.
"The traceability of the individual is compromised which means the traceability of the material is compromised and the whole incidence of cash in the process creates situations where corrupt practices can take place."
While the maximum fine available under current law was £1,000, those committing the crimes could make thousands of pounds, he said, while sentences awarded often "did not reflect the impact".
Labour have urged ministers to toughen regulation by licensing scrap metal dealers, making it easier to close down rogue operators and to examine a ban on cash transactions.
Ian Hetherington, head of the British Metals Recycling Association, said there was a problem with the number of illegal scrap dealers in the UK which could be as many as 900.
The industry accepted regulations needed to be updated, he added, but this would make no difference unless they were properly enforced and there needed to be a uniform approach by the police.
"Frankly if existing law cannot be enforced, new law will not be enforced any better," he said.
"I would not stand in the way of local policing but it does produce a proliferation of well-meaning and relatively short-lived policing initiatives.
"Our members are subject to a different set of criteria set out by the police in Manchester and Lancashire as they are in Kent or in Norfolk. It is a very disjointed picture in terms of policing."