Gas prices for within-day delivery were trading at 37.85 pence per therm at 0836 GMT, up 1.30 pence on Monday's close. Prices for Wednesday delivery were up 0.25 pence at 37.80 pence per therm.
With supply flows at about 156.8 million cubic metres (mcm) per day on Tuesday and demand expected to be about 166.3 mcm, the system was 9.5 mcm undersupplied, National Grid data showed.
A one-day outage at the Teesside Gas Processing Plant (TGPP) processing plant led to lower domestic supply from the UK Continental Shelf, while flows through the Langeled pipeline from Norway to Britain were lower on Tuesday due to slight dip in Norwegian production.
Gas demand in Britain on Tuesday was around 5 percent below the seasonal norm of 175.4 mcm, National Grid data showed, largely due to the warm weather.
Further along the curve, the September contract was 0.17 pence higher at 39.63 pence per therm.
In Britain's power market, prices for day-ahead baseload (24 hours) delivery were trading 0.35 pounds higher at 36.55 pounds per megawatt hour.
There are currently three nuclear reactors offline, with a combined capacity of 1.6 gigawatts.