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By Patrick Graham

LONDON, Dec 5 (Reuters) - Sterling briefly hit its strongest in two months against the dollar on Monday, extending one of the currency world's best performances over the past month as it rode out volatility around Italy's constitutional referendum.

The pound rose 0.1 percent against the dollar to $1.2742 in London, the strongest it has been since before a dramatic drop on Oct. 7, but dipped back to $1.2708.

Dealers said most of the action had centred around volatile moves in the euro following the Italian vote, with importers tempted to buy euros they need to purchase goods from European producers as the single currency sank overnight.

The pound was still up 0.2 percent on the day at 83.66 pence against the euro by 1000 GMT, despite a 1-percent bounce in the euro from overnight lows.

"It all happened in the middle of the night - we saw a full day's trading by 6 a.m. (0600 GMT) but if you weren't in before then, you had missed it," corporate and consumer currency broker Moneycorp's chief executive Mark Horgan said.

"We're mainly an import book, and we saw a lot of guys jumping on the chance to close out (when the euro was low)."

Sterling posted a fifth consecutive week of gains against the euro on Friday, its best run for nine months, as investors' fears eased over a "hard Brexit" that would see Britain lose access to the European Union's single market.

The suggestion by Brexit minister David Davis that the government may be willing to pay into the EU budget in return for access to the bloc's single market also helped it towards levels around $1.30 that it held in August and September.

Many banks are still forecasting further falls in the next quarter around the launch of official talks on leaving the EU.

Whether that happens may depend partly on whether the economy continues to hold up in the face of perceived risks to investment and corporate confidence from the process.

Better-than-expected results from a monthly survey of service sector purchasing managers also pushed sterling a touch higher on Monday.

"It wasn't really enough to move the dial and it does seem like there is two-way interest again on sterling after that huge rise last week," a dealer with one large Asian bank in London said.

"$1.27 will seem to some people like a very good level to get back into pound shorts (bets on it weakening)."

The week's major set-piece domestically is the government's appeal against a court decision requiring parliamentary approval for launching Brexit talks with Brussels.

Confirmation that Prime Minister Theresa May will have to put legislation before parliament, and the noise around the case, may feed the arguments of some analysts that the government is now on course for a softer exit from Europe which disrupts business and banking less than feared.

"The relative outperformance comes from a repricing of Brexit risk, with many feeling more optimistic about the currency's outlook now that talk of access to the single market has come back on the table," LMAX currencies exchange analysts said in a morning note.

(Editing by Louise Ireland) ((patrick.graham@thomsonreuters.com; +44 207 542 9429; Reuters Messaging: patrick.graham.thomsonreuters.com@reuters.net))