* Rising euro, pound hurt shares
* Best euro zone factory data in 17 years
* Majors lifted by oil price rise
* STOXX 600 loses 0.7 percent (Adds closing prices, stocks)
LONDON, Dec 1 (Reuters) - European stocks, which were recovering from early losses and set to finish the first trading day of December in positive territory, fell suddenly after ex-U.S. national security adviser Michael Flynn pleaded guilty to lying to the FBI.
U.S. stocks and the dollar fell as ABC News reported that Flynn was prepared to testify that President Donald Trump directed him to make contact with the Russians.
The news triggered a rise in the euro and in the pound, which hurt stocks as investors questioned the ability of the U.S. president to implement his tax cuts or simply to survive the political storm.
"The old chatter from the summer about President Trump being impeached has surfaced again," David Madden, an analyst at CMC Markets commented.
Britain's FTSE slid 0.36 percent and Euro zone stocks fell 1.06 percent.
Booming data showing euro zone factories had their busiest month for more than 17 years failed to lift euro zone stocks in morning trading.
Oil and gas was among the only sectors to post a positive performance, thanks to rising oil prices after OPEC and other major producers agreed to continue reining in output. BP rose 0.6 percent and Royal Dutch Shell added 0.2 percent.
The Travel and Leisure index also rose 0.31 percent after Deutsche Bank took a positive view of transport stocks and and upgraded Lufthansa and Air France-KLM , which rose 1.3 percent and 0.9 percent respectively.
Dialog, hammered on Thursday by a press report Apple would in-source its power chip design, removing a crucial supplier relationship for the German firm, recovered on Friday to trade up 2.4 percent.
Some healthcare stocks also outperformed. A Morgan Stanley upgrade boosted UCB by 1.6 percent. Novo Nordisk , one of the strategists' pharma favorites, gained 1 percent.
British pharma company Indivior also shot up 11.2 percent after the U.S. Food and Drug Administration approved its opioid addiction drug.
French telecom company Altice - whose shares sank 59 percent in November after disappointing results - gained 0.5 percent after saying it would sell data center and Swiss telecoms businesses to reduce its 50 billion-euro debt .
The high-flying tech sector fell 1.58 percent in a sign of investors' anxiety about parts of the market that have seen stellar performance and inflows this year.
Financials also weighed with Santander losing 2.5 percent, Barclays 2.1 percent and Lloyds 1.9 percent.
The automakers index was down 1.9 percent. Among factors explaining the gloom in the sector, Citi decided to downgrade Peugeot's rating, arguing that "turning Opel around is likely to be costly and time-consuming." The French carmaker fell 2.2 percent.
(Reporting by Helen Reid; Editing by Georgina Prodhan/Mark Heinrich)