UPDATE 1-Britain's FTSE gets leg-up from sterling slide

* FTSE 100 up 0.4 pct

* Sterling slides on construction PMIs, Brexit fears

* Ferguson top gainer after results and buy-back plan

* Sainsbury jumps as Berenberg starts with "buy"

* Tesco rises on investors' hopes of dividend payout (Updates)

LONDON, Oct 3 (Reuters) - Britain's top share index climbed to a near eight-week high on Tuesday, boosted by a slide in the pound after weaker construction sector activity and rumbling uncertainty over Brexit negotiations.

The blue-chip FTSE 100 index ended the day up 0.4 percent, outperforming European markets.

The pound's tumble to a three-week low drove gains in the index dominated by foreign-earning international firms.

Construction sector activity fell in September, and comments from Brexit minister David Davis at the ruling Conservative Party conference added to uncertainty for sterling traders.

"With the makeup of the eventual Brexit deal still unknown, there has been knock-on volatility in sterling and therefore the FTSE 100 - this makes foreign investors more cautious," said Edward Park, investment director at Brooks Macdonald.

UBS Wealth Management chief economist Dean Turner suggested sterling could stabilise at current levels, removing a key support for the large-cap index.

Shrugging aside party conference news and Brexit-related speeches, Turner said: "We choose to focus on the macroeconomic picture which for UK equities is seeing the post-Brexit trend of weaker performing pound, stronger performing FTSE 100, come to an end."

Corporate news also supported the index on the day.

Heating and plumbing product supplier Ferguson jumped 4 percent to the top of the FTSE after reporting a rise in trading profit and a 500 million pound share buyback plan.

Retailers were some of the top gainers, with Sainsbury up 3.5 percent and Tesco up 2.1 percent.

Berenberg initiated coverage of Sainsbury with a "buy", naming the retailer its top pick in a sector it said was facing intensifying competitive and cost pressures.

"With the stock trading at a 15 to 20-percent discount to peers, improving like-for-like momentum could drive a re-rating," Berenberg analysts said.

Tesco rose ahead of its interim results on Wednesday.

"Investors are hopeful it will reinstate dividends although any shareholder returns are likely to be limited," said Neil Wilson of ETX Capital.

Among mid-caps, semiconductor maker Electrocomponents touched a 16-year high after a strong trading update.

Advertising giant WPP was among the worst performers, down 2.1 percent after Morgan Stanley sold 22.5 million shares. The agency's shares are down nearly 25 percent since the beginning of the year.

BAE Systems was also among the biggest losers, retreating 1.7 percent after a downgrade by Berenberg, whose analysts said they expect no organic revenue growth and modest earnings progression in the next two years.

Underpinning index gains were oil majors and financials. (Reporting by Julien Ponthus and Helen Reid; Editing by Mark Heinrich and Andrew Heavens)