UPDATE 3-Sterling hits 2-1/2 year high vs euro as markets price Conservative election win

* Sterling rallies to 84.31 pence per euro, highest since 2017

* Growing confidence in election outcome boosts sterling

* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Updates prices, adds fresh comment)

By Dhara Ranasinghe and Elizabeth Howcroft

LONDON, Dec 5 (Reuters) - Sterling hit 2-1/2-year highs versus the euro on Thursday, on growing confidence that next week's election will give the Conservative Party the parliamentary majority it needs to deliver Brexit, ending near-term uncertainty.

Recent opinion polls suggest the ruling Conservatives will win an outright majority in the Dec. 12 election, removing some of the political uncertainty that has weighed on the currency for the last 3-1/2 years.

Prime Minister Boris Johnson called the snap election to break an impasse in parliament over Brexit. A majority in parliament for his Conservative Party should allow him to get his withdrawal agreement passed by lawmakers and take Britain out of the European Union by the Jan. 31 deadline.

"The broad trend in the polls is not really changing now and the Conservative lead on my poll of polls is about 11 percentage points, which is reasonably sufficient to get them a reasonably decent majority," said Adam Cole, chief currency strategist at RBC Capital Markets in London.

"With only a week to run to the election, if the trend in the polls stays flat, then sterling probably keeps going up."

Sterling was last up 0.2% against the euro at 84.39 pence , but earlier in the day it touched 84.31 pence, its strongest since May 2017. It has gained almost 10% from lows hit in August versus the common currency.

Against the U.S. dollar, the pound rose 0.4% to $1.3144, having climbed as high as $1.3159, a seven-month high, taking its gains since October to more than 7%.

Analysts said the breaching of key technical levels on Wednesday around $1.30 and 85 pence per euro, had accelerated the pound's gains and encouraged traders to cover their short sterling positions.

Investors still say the pound is cheap and could rise further if the Conservatives eventually secure a majority in parliament.

Marco Pabst, chief investment officer at asset manager Union Bancaire Privee, said the pound's discount was between 20% and 30%.

"Once we have political stability in the country and this kind of implies a bigger Conservative-run government, I think this discount should narrow over the foreseeable future," he said.

The latest Reuters poll also suggested investor sentiment towards one of the most battered major currencies in recent years is turning.

Almost all foreign exchange strategists surveyed were reasonably or very confident that Britain would leave the EU with a deal. The poll of nearly 60 foreign exchange strategists found sterling would rise 3% to $1.35 in 12 months.

That compares with a $1.32 forecast made a month ago.

In a sign of near-term caution, one-week implied volatility on sterling, a contract straddling the election, rose to its highest since late October.

(Reporting by Dhara Ranasinghe; Editing by Christina Fincher and Mark Potter)