The within-day contract was up 1.25 pence at 34.00 p/therm by 0930 GMT.
The day-ahead contract was up 1.45 pence at 33.75 p/therm.
The average temperature in Britain is expected at 3.8 degrees Celsius on Tuesday, 1.7 degrees lower than previously expected, rising to 4 degrees on Wednesday, Eikon Refinitiv data showed.
Britain's gas market was 43 million cubic metres (mcm) undersupplied on Tuesday morning, with demand forecast at 339 mcm, above the seasonal norm. Supply flows were forecast at 296 mcm, National Grid data showed.
An outage at Centrica's Barrow gas treatment plant on Tuesday reduced supply capacity by 7.7 mcm per day, but was expected to end the same day, National Grid website showed.
Gas for power generation was expected to rise by 6 mcm/day on Tuesday from Monday, but it was expected to fall on Wednesday due to forecasts for higher output from wind power turbines.
Peak wind power generation is forecast at 4 gigawatts (GW) on Tuesday, rising sharply to 13 GW on Wednesday, Elexon website showed.
Sendout from the country's LNG terminals was nominated at 69 mcm on Tuesday, 19 mcm lower than the previous day, Refinitv data showed.
"We expect LNG to be adjusted higher tomorrow as South Hook and Dragon get a few cargo arrivals which are already waiting outside ports," analysts at Refinitiv said.
LNG supply is expected to ramp up over the next few weeks, with around 16 tankers set to arrive to Britain before the end of the month.
UK gas imports from Norway via the Langeled pipeline were up by 5 mcm/day on Tuesday from the previous day.
Further out on the curve prices also rose.
The January gas contract was up 1.70 p at 37.10 p/therm.
The summer 2020 contract was up 0.95 p at 33.40 p/therm.
The day-ahead gas price at the Dutch TTF hub was up 0.25 euro at 12.85 euros per megawatt hour.