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* FTSE 100 up 0.4 pct
* Capita jumps 13 pct as green shoots appear
* Investors eye signs of softer Brexit stance
* LSE boosts financials after bullish update
LONDON, June 13 (Reuters) - British shares gained on Tuesday as a sell-off in the tech sector petered out worldwide, financials supported gains and outsourcing company Capita soared as its outlook brightened.
Relief was palpable after Monday's dip, which hit UK tech firms Micro Focus and Sophos, but trading remained muted with the FTSE 100 up just 0.2 percent as investors continued to sift through the fall-out from Britain's election.
"There's a tendency to turn to one factor and attribute it to that, but people always just get nervous when valuations get very high, as they did with these companies," said Laura Foll, UK Equity fund manager at Henderson.
Capita jumped 12.5 percent to its highest level in eight months after its trading update suggested green shoots of recovery were appearing.
The outsourcing firm was set for its best day in 17 years as analysts praised progress in its efforts to restructure the business which has suffered a string of profit warnings and demotion from the blue-chip index.
"Capita's pre-close interim management statement points to progress on many fronts as Capita works through a "transitional" year," said UBS analysts.
Capita helped mid-caps gain 0.5 percent, outperforming the blue-chips.
The morning after Prime Minister Theresa May's grilling by Conservative MPs following a disastrous election, investors eyed the shifting sands and looked for signs the government's stance on Brexit was softening.
"There seems to be a shift towards staying in the single market and the customs union," said Foll. "That would be pretty significant for our portfolio if it did prove to be true."
London Stock Exchange led the FTSE higher after the firm said it expected growth, shrugging off the disappointment of a scuppered merger with Deutsche Boerse.
Merlin fell to the bottom of the index after the entertainment company behind Madame Tussaud's waxworks museum and Legoland said militant attacks in London and Manchester had dented demand.
The company's shares have been the most sensitive to recent attacks.
Ashtead gained 1.6 percent as growth in its core North American market boosted its profits for the year, and the firm said it had seen good seasonal uplift to its industrial equipment rental business.
"Ashtead sees good markets with a seasonal uplift in volumes, and we see little change to consensus," said UBS analysts. "Trading remains strong, but without guidance upgrades we believe valuation looks exposed."
Meanwhile, among mid-caps, oil services firm Petrofac gained 5.8 percent, among the top European stocks, boosted by a $35 million contract with the Kuwait Oil Company.
Property company Kennedy Wilson Europe jumped 9 percent after its U.S. parent company sweetened a deal to buy it back.
(Editing by Ed Osmond)