By Jemima Kelly

LONDON, Dec 6 (Reuters) - Sterling hit a two-month high against the dollar on Tuesday, with investors betting the British government would lose its battle to trigger the Brexit process without parliamentary approval.

The government is seeking to overturn a decision in the High Court last month that could derail its Brexit plans. The court ruled that Prime Minister Theresa May could not trigger Article 50 of the Lisbon Treaty and begin two years of Brexit talks with the other EU members without parliamentary backing.

The pound surged after November's ruling, investors believing that greater parliamentary involvement would reduce the chances of a "hard Brexit" in which tight controls on immigration are prioritised over European single market access.

Sterling has climbed almost 6 percent against the dollar since the start of October, when it was trading around $1.20 GBP=D4 on expectations for a hard Brexit - a view driven in large part by comments from May and other senior members of the ruling Conservative party at its annual conference.

November's court ruling - as well as the suggestion last week 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 - have helped the pound rise to five-month highs against the euro EURGBP=D4 , though it was slightly off those highs on Tuesday at 84.37 pence.

Against the dollar, sterling climbed 0.4 percent to hit $1.2775, its highest since Oct. 6. Better-than-expected results from a monthly survey of service sector purchasing managers also pushed sterling a touch higher on Monday.

"The government really does have to argue this one extremely well if it's going to overturn that position - that's the view of the market," said Rabobank currency strategist Jane Foley.

"However, there is a huge amount of uncertainty around that, and from that point of view I think sterling is at the very least likely to see a lot of volatility and still remains pretty vulnerable. I think there's limited upside potential from these levels."

The hearing is due to last for four days but the verdict is not expected until January.

"The expectation is that the government is going to lose the case," wrote BNP Paribas currency strategists in a research note. "The first day of testimony saw the government's lawyer face tough questioning from the justices... We remain exposed for a continued squeeze of short sterling positions."

(Editing by Jeremy Gaunt.) ((jemima.kelly@thomsonreuters.com; +44)(0)(20 7542 7508; Reuters Messaging: jemima.kelly.thomsonreuters@reuters.net))