* Formal Brexit process begins
* Sterling under pressure
* Stocks regain footing
By Jamie McGeever
LONDON, March 29 (Reuters) - European shares drifted lower on Wednesday, while sterling battled back from a one-week low and regained its composure amid the drama of Britain formally triggering its exit process from the European Union.
The pound was the biggest loser on major currency markets as European trading got underway. But it clawed back almost all its losses after a draft EU document made no mention of the possibility that the two sides will fail to strike a deal.
"What is priced in at the moment is a hard Brexit, so if there is something being constructed by the EU that is a little softer, that would send sterling sharply higher," said Mizuho's head of hedge fund FX sales, Neil Jones.
Prime Minister Theresa May will notify EU Council President Donald Tusk in a letter that Britain really is quitting the bloc it joined in 1973, pitching the United Kingdom into the unknown and triggering years of uncertain negotiations.
The start of the formal Brexit process comes a day after the Scottish Parliament backed a bid to hold a second independence referendum that could break up the UK, adding another layer of uncertainty for investors to navigate.
The longer term picture may be a more volatile one.
"Sterling will be incredibly sensitive to negotiations and will offer a clear gauge of how things are panning out. We could see it move lower still if negotiations take a sour turn - $1.10 is feasible," said Neil Wilson, senior markets analyst at ETX Capital.
Sterling hit a one-week low of $1.2378 earlier, but was last trading down 0.1 percent against the dollar at $1.2432.
Elsewhere in currencies, the euro was down a fifth of one percent at $1.0793 and the dollar was down slightly against the yen at 111 yen.
The dollar bounced from 4-month lows as a top Federal Reserve official talked of more rate hikes to come. Fed Vice Chairman Stanley Fischer, one of the more influential policymakers with markets, said two more rate increases this year seemed "about right".
In stocks the leading index of 300 European shares gave up all its early gains to trade down 0.1 percent at 1,486 points, while Germany's DAX halved its gains to trade up 0.3 percent.
Britain's FTSE 100 fell 0.2 percent as sterling bounced back from its one-week low.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3 percent and back toward recent 21-month peaks, while Japan's Nikkei added 0.1 percent.
The Dow Jones snapped an eight-day losing streak on Tuesday, its longest run of losses since 2011, in part as a survey showed consumer confidence surged to a more than 16-year high.
S&P 500 futures pointed to a flat open on Wall Street.
"Economic fundamentals still remain exceedingly sound here in 2017 and you do not need Trump's pro-growth fiscal agenda for this to be one of the best years for growth since the recovery started," argued Tom Porcelli, chief U.S. economist at RBC Capital Markets.
"We still think tax reform happens, but you are better off thinking about the timing as an end of year event at best."
In commodity markets, oil prices gained after a severe disruption to Libyan oil supplies and as officials suggested the Organization of the Petroleum Exporting Countries and other producers could extend output cuts to the end of the year.
U.S. crude CLc1 added 0.4 percent to $48.57 a barrel, while Brent rose 0.5 percent to $51.57.
Spot gold was little changed at $1,251 an ounce.
Additional reporting by Wayne Cole in Sydney and Jemima Kelly in London; Editing by Jeremy Gaunt