LONDON, July 21 (Reuters) - British gas prices rose early on Thursday as hot weather drove demand, while Dutch prices dropped after physical flows through Russia's biggest gas pipeline to Germany resumed after a 10-day outage.

The British day-ahead contract rose by 4.5 pence to 272.50 pence per therm by 0853 GMT while the within-day contract rose by 17 pence to 265 pence per therm.

Strong power demand to keep houses cool, combined with slow wind speed and weak French nuclear output, kept demand high and put pressure on the UK system, Refinitiv analysts said.

Britain’s gas system was undersupplied by 3.4 million cubic metres (mcm), National Grid data showed.

However, a rise in Norwegian gas nominations to Britain put some pressure on the prices.

The flows were expected to remain stable "with a light maintenance schedule ahead with no notable cuts until Aug. 13," Refinitiv said.

In the Dutch market, however, prices eased after the restart of the Nord Stream 1 gas pipeline after annual maintenance.

The pipeline accounts for more than a third of Russian gas exports to the European Union.

The front-month gas contract fell by 12.50 euros to 149 euros per megawatt hour (MWh), while the contract for September delivery was down 6.80 euros to 151.50 euros/MWh.

"With the restart of the NS1 pipeline, although still only at 30% of its original capacity, the TTF gas price future has eased somewhat compared to previous days," Hans van Cleef, senior energy economist at ABN Amro, said.

"Still whilst trading just below 150 euros per MWh, prices are still extremely high for the time of the year," he added.

Meanwhile, eastbound gas flows via the Yamal-Europe pipeline to Poland from Germany increased, operator data showed.

Peak wind power generation in the United Kingdom is forecast at 5.8 gigawatts (GW) on Thursday, falling to 1.5 GW on Friday compared with total metered capacity of around 20 GW, Elexon data showed.

In the European carbon market, the benchmark contract rose by 0.44 euros to 79.28 euros a tonne.

(Reporting By Susanna Twidale; editing by Nina Chestney and Barbara Lewis)