Prices for next-day delivery rose to 58.35 pence per therm at 0808 GMT, up 0.90 pence from the previous settlement.
Gas for immediate delivery was 0.55 pence higher at 58.25 pence per therm.
Temperatures are forecast to be around 3 degrees Celsius on average in Britain on Tuesday, 3 degrees below normal levels for the time of year.
Gas consumption at local distribution zones (LDZs) is expected to be higher than on Monday to fuel demand for central heating systems. Britain's National Transmission System delivers gas to 13 LDZs across the country, which transmit gas to end-users.
The cold snap is not expected to last, however, as temperatures are forecast to return towards normal levels by Wednesday, which should reduce demand.
The UK gas system was largely balanced as of 0700 GMT on Tuesday. Flows were expected to be 297.5 million cubic metres/day, while demand was 298.6 mcm, National Grid data showed. Seasonal normal demand is 270.0 mcm.
In the Dutch TTF gas market, prices also were higher due to forecasts for higher consumption levels for Germany and the Netherlands over the next two weeks.
Day-ahead TTF gas was up 0.10 euros at 24.10 euros per megawatt hour, while within-day TTF rose by 1.15 euros to 24.30 euros per MWh.
In Europe's carbon market, benchmark EU Allowances (EUA) inched down by 0.01 euro to 7.04 euros per tonne.