* STOXX 600 up for third straight session
* Indexes extend gains after May confirmed as British PM
* Thyssenkrupp and ArcelorMittal among top performers
* Goldman Sachs keeps "neutral" view on equities (ADVISORY- Follow European and UK stock markets in real time on the Reuters Live Markets blog on Eikon - see cpurl://apps.cp./cms/?pageId=livemarkets)
By Alistair Smout and Sudip Kar-Gupta
LONDON, July 11 (Reuters) - A top European share index rose on Monday to post its highest close since Britain voted to leave the European Union, after Theresa May won the race to succeed David Cameron as Prime Minister, reducing political uncertainty in the UK.
May's rival for the leadership, Andrea Leadsom, pulled out of the race on Monday, and Cameron said he would resign on Wednesday to hand over to May and avoid a leadership vacuum over the summer.
The STOXX Europe 600 closed up 1.6 percent at 332.72, its highest close since June 23, the day of the referendum. However, the index remains 4 percent below that closing level, after the result sent shares tumbling on concerns over the outlook for the British and euro zone economies.
Analysts said May was an experienced politician who would provide stability during the Brexit negotiations
"The difference between Theresa May and her counterpart was that she has a disciplined approach and a proper strategy for Brexit. The alternative was uncertain," Ankit Gheedia, equity and derivative strategist at BNP Paribas, said.
"We know she has experience, and is a bit more strategic, so the market is relieved on the back of that."
FTSE 250 mid caps, which have high exposure to the UK economy, ended 3.3 percent higher.
Blue chip British housebuilders, such as Barrat Developments and Berkeley, ended 7-8 percent higher. In all, the FTSE 100 ended up 92.22 points, or 1.4 percent, at 6,682.86 points.
A rally in the shares of steelmakers also helped European stocks to rise for the third straight session, with the sector lifted by signs of sector consolidation.
ThyssenKrupp, Germany's biggest steelmaker, said it was in talks with India's Tata Steel about a consolidation of beleaguered European steel mills that are hit by overcapacity, weak demand and cheap imports.
The prospect of sector consolidation pushed up Thyssenkrupp shares by 6.4 percent, while rival ArcelorMittal also climbed 5.6 percent.
Shares in Italian bank Monte Paschi also rose 6.9 percent, with Italian newspapers reporting that bank rescue fund Atlante will soon take on an additional role to soak up bad loans from Monte Paschi.
Despite signs of a possible stabilisation in British politics, Goldman Sachs' strategists kept a "neutral" view on equities. They cited concerns over a generally weak economic backdrop, with the Brexit vote expected to hit the British economy.
"We remain defensive in our asset allocation and believe the positioning-driven recovery of risky assets, in particular for equities, post Brexit is likely to fade," said Goldman.
"We still believe equities are fragile and stuck in their 'fat and flat' range with little return potential but potential for drawdowns," it said. (Editing by Janet Lawrence)