The within-day contract rose 0.45p to 28.25 p/therm by 0920 GMT.
The day-ahead contract traded flat to its Monday level at 28.00 p/therm.
The UK gas system was 22.4 million cubic metres (mcm) undersupplied, with demand forecast at 312.4 mcm and supply at 290 mcm/day, National Grid data showed.
Undersupply is due to a rise in gas demand for heating following colder weather.
Residential gas demand was expected to be at 248 mcm on Tuesday, 25 mcm higher than previously expected, Refinitiv data showed.
Average UK temperatures were forecast to drop to 3.7 degrees Celsius on Tuesday, which is 1.9 C degrees lower than expected earlier, the same data showed.
Residential consumption is predicted to reduce on Wednesday, however, as temperatures are forecast to rise to 4.6 C Celsius, which has put pressure on the day-ahead price.
But warm weather will not last as long as previously expected, Refinitiv analysts said in a morning note. "Temperatures should drop below seasonal normal again from the mid of next week," they said.
Gas-for-power demand is seen reducing throughout this week.
Peak wind generation is forecast at over 12 Gigawatts (GW) on Tuesday and Wednesday, Elexon data showed. Total wind generation capacity in Britain is 15.3 GW.
On the supply side, flows from Norway rose to 94 mcm on Tuesday from 87 mcm on Monday, Gassco data showed.
Flows from the UK Continental Shelf were 2 mcm higher than in the previous day.
LNG sendout was at 72 mcm on Tuesday, which is a big drop from last week's level of over 120 mcm/day.
Five tankers are expected in Britain in February so far.
The February contract was up 0.30p at 27.70p/therm.
The day-ahead gas price at the Dutch TTF hub was up 0.17 euro at 10.65 euros per megawatt hour.
The benchmark Dec-20 EU carbon contract was flat at 24.59 euros per tonne.