Two cargoes from Qatar have arrived in the past week, with a third on its way and a further tanker due to arrive at Milford Haven in Wales within the next few days.
The arrivals come as UK households and businesses used 20% more gas than normal in March, given the cold conditions.
The demand saw stocks of stored gas fall to 10% of capacity, given the pressure on supply. This time last year stores were almost half full.
Britain is more vulnerable than other countries to gas shortages because of its small storage capacity, which holds just 15 days worth of energy supplies.
Andrew Horstead, of Utilyx energy consultancy, said it was important to stress that stored gas made up only a share of the UK's energy supply.
He said the gas cargo now arriving from overseas would be fed straight into the supply network, with consumers likely to ease pressure on usage over the next fortnight.
Despite the continuing cold weather, Mr Horstead said the change in the clocks would assist in reducing the need for heat and light.
He said: "The weather has helped to encourage flows into the UK and that will take a little bit of pressure off the system. The end usage is also expected to fall off in April, which will also help."
Mr Horstead said premium prices were still being paid, at 90p per therm, compared to 60p per therm paid in 2010 and early 2011.
He added that prices were kept high due to the continuing impact of the nuclear power crash in Japan following the earthquake in March 2011, with further demand on supply coming from Taiwan, Korea and Brazil.
Recent transportation problems of gas caused by an interconnecter fault in the UK at the end of last week also raised concerns about supply.
A spokeswoman for National Grid said supply was now comfortable after markets reacted on Friday to high demand.