* Sterling wallows below overnight lows
* Dollar gains vs yen, pushes toward last week's highs
* Market awaits Fed minutes, Yellen speech this week
TOKYO, Oct 11 (Reuters) - The dollar firmed in early Asian trading on Tuesday, while recently beleaguered sterling wallowed close to recent lows on continuing fears about the likely impact on Britain from exiting the European Union.
Japanese, Canadian and some U.S. markets were closed on Monday for holidays.
The pound was down 0.1 percent against the dollar at $1.2347, below its overnight low of $1.2345, in the wake of Friday's "flash crash" that sent it hurtling to its lowest levels in 31 years.
"Economic data does not help very much to explain sterling's movement. The fact of the matter is that the UK has fared well in the three and half months since the referendum," wrote Marc Chandler, global head of currency strategy at Brown Brothers Harriman.
"The depreciation of sterling will have an impact on the UK current account balance," he said. "It will be reduced, but do not be surprised if it comes from reduced volume of imports as much as an increase in value of exports."
Meanwhile, Japan's current account surplus stood at 2.0 trillion yen ($19.3 billion) in August as the trade balance swung to a surplus due to falling imports, Ministry of Finance data showed on Tuesday.
The figure was larger than economists' median forecast for a surplus of 1.54 trillion yen in a Reuters poll.
The dollar was last up 0.3 percent against the yen at 103.92 yen, shy of last week's high of 104.17 but above Monday's low of 102.80 yen.
The euro edged down slightly to at $1.1134.
The dollar index, which tracks the greenback against a basket of six major rivals, added 0.1 percent to 96.987.
Looking ahead, investors awaited Wednesday's release of minutes of the Federal Reserve Open Market Committee's September meeting, which they will parse for clues as to how close the U.S. central bank is coming to hiking interest rates.
Market participants were pricing in around a 70 percent chance that the Fed will raise rates in December, according to CME Group's FedWatch program.
U.S. retail sales data on Friday could offer some insight on the strength of consumption. Later that day, Fed Chair Janet Yellen will address a Boston Fed economics conference. (Reporting by Tokyo markets team; Editing by Eric Meijer)