* Gas system oversupplied by 13 mcm
* Milder weather outlook for this week
* UK's summer gas season starts on April 1
March 29 (Reuters) - British prompt gas prices fell on Tuesday morning on an oversupplied system as domestic supply and imports from Norway were strong, and demand softened due to milder weather.
Gas for immediate delivery fell by 1.3 pence or 4.3 percent to 28.70 pence per therm by 0930 GMT, while the day-ahead contract fell by 0.57 pence or 1.9 percent to 28.80 pence/therm.
Both nominated pipeline supplies from the UK continental shelf (UKCS) and LNG terminals were high on Tuesday morning at 143 mcm and 42 mcm respectively.
Imports from Norway were up by 10 mcm to 109 mcm compared to the last trading session on Thursday.
The long system, combined with a comfortable supply outlook for the coming weeks and confirmation of additional LNG shipments, have pushed prompt prices lower, traders said.
One LNG tanker arrived to South Hook terminal on Monday, and two more are expected to arrive over the next week.
Meanwhile, demand for gas has softened as temperatures are expected to rise later this week, and overall were seen to average normal with some warmer spells at times, UK's Met Office said.
The summer gas season is due to begin on April 1 which will run until October. This is typically a period of lower demand for gas due to warmer temperatures and a time when many gas infrastructure operators carry out maintenance.
Further out on the curve, the contract for gas delivery next-season fell 0.56 pence or almost 2 percent to 27.70 pence/therm.
Dutch day-ahead gas prices eased 0.12 euro/MWh to 12.10 euro/MWh. In the European carbon market, front-year allowances eased 0.09 euro or 1.9 percent to 4.77 euro a tonne.
(Reporting by Nerijus Adomaitis in Oslo; editing by Nina Chestney)