* Nickel price touches highest since September 2019

* LME tin spread at tightest since last June

* LME aluminium stocks fall to fresh low since last April

LONDON, Jan 7 (Reuters) - Copper prices hit their highest levels since 2013 on Thursday for a third straight day, driven by expectations of infrastructure spending by incoming U.S. President Joe Biden after his party won control of the Senate.

Three-month copper on the London Metal Exchange had gained 1.5% to $8,160 a tonne by 1710 GMT, after touching $8,182, its highest since February 2013, following similar peaks in the two previous sessions.

Copper on Comex added 1.2% to $3.70 a lb.

Democrats on Wednesday completed a sweep of two U.S. Senate seats in Georgia, giving the party control of the chamber and boosting Biden's plans to spend $2 trillion on infrastructure.

"The overwhelming theme is the reflation trade at the moment. With the Democratic Party having control of Congress there's more room to get its bills approved," Xiao Fu, head of commodity market strategy at Bank of China International, said.

"Financial markets are pricing in quite a strong recovery and there's optimism about infrastructure stimulus."

* LME nickel hit its highest since September 2019 at $18,060 a tonne, up 1.6%, after stainless steel futures surged as much 5% in China and inventories in the country slid.

Nickel is mainly used in making stainless steel. "We understand that onshore (Chinese) stainless steel prices have been supported by firm downstream demand as well as low inventory," Alastair Munro at broker Marex Spectron said.

* The premium of cash LME tin over the three-month contract rose to $229 a tonne on Wednesday, the highest since June last year, indicating tightness in LME inventories, which have tumbled 67% over the past three months.

* LME aluminium inventories fell to their lowest since April 2020 at 1.31 million tonnes while the U.S. aluminium premium rose to its strongest since Sept. 16 at $329.33 a tonne.

* LME aluminium shed 0.3% to $2,033.50 a tonne, zinc gained 0.8% to $2,884, lead fell 1.4% to $2,034 and tin rose 0.02% to $21,110.

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($1 = 6.4555 yuan) (Additional reporting by Mai Nguyen in Hanoi; Editing by Kirsten Donovan, Alex Smith and Jan Harvey)