FTSE 100 up 1.7 pct Sterling sinks further after May lays down...

• FTSE 100 up 1.7 pct
• Sterling sinks further after May lays down gauntlet to EU
• Banks and miners drive gains
• Just Eat tumbles on report Uber in talks to buy Deliveroo

(Updates prices, adds details, quotes)

A slide in sterling after a speech by Prime Minister Theresa May helped boost Britain's exporter-heavy FTSE 100 to a 2 1/2 week high, cementing a three-day rally driven by banks, miners and oil stocks as investors' fears of a trade war faded.

On the corporate front, Just Eat shares tumbled as Uber's reported advances to Deliveroo triggered fears of rising competition in the food delivery industry.

The FTSE 100 .FTSE ended the day up 1.7 percent, extending early gains as developments on the Brexit front sank sterling, supporting the index whose constituents mainly earn outside the UK.

The pound tumbled two cents against the dollar, set for its biggest daily drop this year, after Prime Minister Theresa May said Brexit talks with the European Union had reached an impasse and called for new proposals.

"The near-term path of UK stocks and sterling is highly dependent on the Brexit newsflow and as a result we maintain an underweight position to both, instead favouring themes and geographies with more economic certainty," said Edward Park, investment director at Brooks Macdonald.

The FTSE 100 had its third day of gains in a row - its longest winning streak since mid-August. The index has been struggling for momentum as Brexit negotiations wear on.

A rare faller in a strong market, food delivery company Just Eat JE.L tumbled as much as 7.5 percent after a report that Uber was in early talks to acquire its rival Deliveroo.

"Uber’s deep pockets combined with an acquisition puts a lot of competitive pressure on the other food delivery companies over the medium term," said Brooks Macdonald's Park.

European benchmarks all climbed as investors piled into stocks in relief that U.S.-China tariffs announced this week were lower than feared.

Investors also believed their impact on global growth would be muted, save for a slight increase in inflation - which is a negative for bond markets but a positive for equity markets.

Overall, banks were a top driver of FTSE 100 gains. Heavyweight banking stock HSBC HSBA.L was the biggest boost to the index, up 1.3 percent, driven higher by a spike in the Hong Kong dollar overnight caused by expectations of a rise in bank lending rates and tightness in cash supplies.

Standard Chartered STAN.L , which also has significant exposure to Asia, also gained 1.8 percent, among top FTSE risers.

Mining stocks Glencore GLEN.L , Anglo American AAL.L , Rio Tinto RIO.L and BHP Billiton BLT.L rose 2 to 3 percent as metals prices added to this week's gains.

Copper hit its highest in six weeks and was set for its biggest weekly climb in 15 weeks as investors expected trade tariffs to have less impact on global growth than some had feared.

"Our economists expect trade disputes to linger with no resolution in sight, but China plans to offset the headwinds with infrastructure spending and liquidity support," Goldman Sachs analysts wrote, adding that they see room for copper to rise further.

Oil majors BP BP.L and Royal Dutch Shell RDSa.L also spurred the FTSE 100 higher as crude prices rose ahead of an OPEC meeting on Sunday.

Shares in industrial group Smiths SMIN.L fell 4.9 percent, the top FTSE 100 fallers.

Smiths reported full-year profit which missed analysts' estimates due to short-term problems at its medical unit due to the loss of some product certifications under new European regulations.

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