Chris Train from National Grid says the system has held up very well
The UK has the equivalent of eight days worth of gas usage left in storage, the Conservative Party has claimed.
Shadow energy secretary Greg Clark called for more storage capacity and said the UK lacked "essential back-up plans".
But speaking to the BBC, National Grid said: "Be assured, the gas isn't going to run out."
Demand for gas was a third higher than normal on Monday due to the weather, prompting the Grid to issue an alert.
About 441 million cubic metres of gas was demanded on Monday which made it one of the highest gas demand days. The record demanded on one day was 449 million cubic metres on 7 January 2003.
The government accused the Conservatives of "scaremongering".
Shadow energy secretary Greg Clark says there is only enough stored gas for eight days
"There is no risk of consumers being cut off. The system has in fact been responding extremely well. Britain has a vast amount of storage - it's called the North Sea," said a government spokesman.
Centrica, the parent company of British Gas, agreed with the the government that the system was coping. Its chief executive, Sam Laidlaw, said: "While we are by no means complacent, and watching the situation closely, the evidence is that the UK gas market is currently operating well in the face of severe weather and unprecedented demand. "
Gas storage is like an insurance policy, BBC correspondent Nils Blythe said, which safeguards against extreme events.
"Britain has less gas storage than many other countries and therefore would be more vulnerable in extreme circumstances," he said.
"But those extreme circumstances have not arrived yet."
Traditionally, demand for gas is highest in the first week of January that at any other time of the year, as people return to work and school after the Christmas period.
However, because of the particularly cold start to 2010, and a problem with an offshore supplier, the National Grid issued an emergency Gas Balancing Alert on Monday, which is triggered when gas demand outstrips supply.
We simply cannot continue to rely on unpredictable overseas supplies
Tom Foulkes, Institution of Civil Engineers
This was only the second time the operator has done this. The first time was in 2006.
The alert tells big gas users, such as power plants, to curb demand.
Big generators, such as E.On, have both gas-fired and coal-fired power stations and can choose to switch between the two.
At the same time, extra gas supplies were rushed out to the liquefied natural gas importation terminal in Kent through pipelines in Belgium and Norway.
The National Grid said these moves had stopped any risk of a gas shortage.
The Conservatives blamed the government for having its "head in the sand" over the issue of gas storage.
"When will the government understand we need more storage capacity and the ability to get gas to consumers so nobody has to face the possibility of going without gas during cold snaps like this one?" said Greg Clark, shadow energy and climate change secretary.
According to the Institution of Civil Engineers (ICE), the situation highlights the UK's dependency on imported gas.
"To avoid energy crises and price hikes in the future the UK energy sector must urgently build extra gas storage capacity into the network. We simply cannot continue to rely on unpredictable overseas supplies," said Tom Foulkes, director general of ICE.
Responding to the claims, National Grid's national operations director Chris Train sought to reassure the public.
"We've got supplies coming into the UK that are comfortable in terms of meeting these high levels of demand, looking forward. I would always encourage people to use their energy efficiently but, be assured, the gas isn't going to run out," he said.
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