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* Graphic: sterling and gilt yields bit.ly/2dgAXn1
* Graphic: World FX rates in 2016 tmsnrt.rs/2egbfVh
By Jemima Kelly
LONDON, Nov 29 (Reuters) - Sterling inched up against the dollar on Tuesday, staying in the broad $1.23-$1.26 range it has traded in for the past two weeks, with investors waiting for fresh cues on how Britain will leave the European Union.
The pound got a small boost on Tuesday after data showed lending to Britons expanded last month at the fastest annual pace in 11 years, while mortgage approvals were stronger than expected, bolstering the picture of resilient consumer demand after June's Brexit vote.
Against a broadly weaker euro, sterling climbed 0.7 percent to trade back below 85 pence, having just recorded its longest run of weekly gains since early 2015 against the single currency.
Sterling is still almost 10 percent weaker against the euro compared with before Britain's vote to exit the European Union. But it has climbed 5 percent since the start of November, as the euro has weakened on uncertainty over an Italian constitutional referendum on Sunday and French and German elections next year.
"There remains concern about the Italian referendum and I think that's likely to continue to dominate activity in Europe for the next few days - that's probably why sterling is stronger against the euro," said Societe Generale currency strategist Alvin Tan.
The way in which Britain exits the EU has dominated sterling's direction since the vote to leave in June. With few new clear developments in recent weeks, analysts said the currency was treading water.
The British government denied on Tuesday that a document photographed in the hands of an official from the ruling Conservative party - which said the strategy for Brexit talks was to "have cake and eat it" - accurately reflected its plans for forthcoming EU divorce negotiations.
The handwritten note also said Britain would be unlikely to stay in the European single market, and that the government was "loath" to bring in "transitional" arrangements.
It suggested Britain could seek a "Canada Plus" deal - a reference to a trade deal agreed between Canada and the EU last month after seven years of talks.
Against the dollar, sterling climbed 0.4 percent to $1.2458 .
Data from the Commodity Futures Trading Commission released on Monday showed speculators' bets against sterling fell for a second straight week, to the lowest since September.
"Sterling short positioning continued to fall last week, mainly in the absence of any fresh selling triggers," wrote Credit Agricole currency strategists in a research note.
"Given stable BoE (Bank of England) monetary policy expectations, and as political uncertainty is unlikely to increase in the short-term, the risk of additional position squaring is likely to continue intact."
The BoE cut interest rates to a record low of 0.1 percent in the aftermath of Brexit, and is expected to keep them there for all of 2017. (Editing by Tom Heneghan)