LONDON- Sterling hovered above $1.33 on Monday as traders clung to hopes that Britain and the European Union would soon seal a long-awaited Brexit trade deal, even as the clock ticked down on the Brexit transition period.

The United Kingdom exits the EU's orbit on Dec. 31 and both sides are demanding concessions from the other on fishing, state aid and how to resolve any future disputes before agreeing a deal to govern their trading relationship from Jan. 1.

British Environment Secretary George Eustice said that this week was "crucial" to get a breakthrough in talks and that time was running out. 

Despite the failure to reach agreement so far, most sterling investors are confident the two sides will eventually come around - the pound has held on to recent gains and last week hit a 2-1/2 month high.

On Monday, the British currency rose to as high as $1.3355 GBP=D3 before falling back to trade at $1.3316, unchanged on the session.

Against the euro, the pound slipped 0.1% to 89.91 pence EURGBP=D3 .

Not everyone is convinced that the pound will move much higher should a deal be clinched.

"The UK is likely to face adjustment pressures from the twin factors of COVID-19 and Brexit with or without a limited FTA (Free Trade Agreement) in place from January 1, 2021, and there is scope for more friction in the bilateral UK/EU relationship going forward," said Stephen Gallo, European Head of FX Strategy at BMO Capital Markets.

Gallo has a one and three-month target of $1.34.

"Regardless, the UK's twin fiscal and current-account deficits will probably curb GBP appreciation for the time being, and their persistence could pose medium-term inflation risks to the UK economy," he added.

(Reporting by Tommy Wilkes; Editing by Pravin Char) ((thomas.wilkes@thomsonreuters.com))