* Russian gas flows to Ukraine continue until at least June 9
* Mild weather to dominate UK for most of June
LONDON, June 2 (Reuters) - British wholesale natural gas prices dropped to their lowest in more than 3-1/2 years on Monday as Russia and Ukraine reached a temporary gas supply deal, while healthy alternative supplies and warm weather also added downward pressure.
Gas for delivery within the day traded at 41.50 pence per therm at 0850 GMT, its weakest price since October 2010 and a third lower than at the start of the Ukraine crisis in late February.
"All signs from Russia and Ukraine are for compromise and against cutting gas supplies. Adding to that, we've got very mild weather, healthy storage and good LNG imports, so that's further weighing on prices," one gas trader said.
Russia's Gazprom gave Ukraine on Monday an extension into next week to resolve the gas price dispute at the heart of the two countries' confrontation, a day before Moscow was due to turn off the taps unless Kiev paid in advance.
"Less concern over a Russia-Ukraine gas cut is also pulling down prices for next winter, when a supply cut would hit markets hardest. Also, Brent oil prices are back below $110 a barrel, removing further support from seasonal contracts," the trader said.
Gas prices for delivery next winter were down 1.02 pence at 59.78 pence a therm.
On the supply side, tankers with enough gas to meet almost three days of current British demand are scheduled to arrive in the UK this week.
At the same time, gas demand is entering its lowest season of the year as mild weather cuts the need for residential heating, which makes up a large chunk of British consumption.
Meteorologists said they expected British average temperatures to rise above the seasonal norm of 13-14 degrees Celsius by June 6 and remain warmer than average until at least the middle of the month. (Reporting by Henning Gloystein; Editing by Dale Hudson)