LONDON- Sterling hit a one-week high on Tuesday despite a broadly steady dollar as three days of negotiations on Britain's trade agreement with the European Union began in Brussels with some analysts growing hopeful of a deal.

Talks on a joint legal text of trade agreement, which will also cover energy links and transport, will last until Friday morning. EU negotiators have signalled that they are willing to begin work on a joint legal text of trade agreement before talks resume, The Times reported on Tuesday.

"This week is a very, very important week for the pound as we slowly grind toward the day of true Brexit," according to MUFG analysts.

"In negotiations and given the political capital that (Prime Minister Boris) Johnson is losing in the fight against COVID we see the balance as having shifted more in favour of a deal."

Sterling was 0.3% higher at $1.2866 at 1115 GMT after hitting $1.2878 earlier in the trading session. In contrast, most other currencies, including the euro and the yen, were weaker against the dollar. It was also 0.2% higher versus the euro at 91.04 pence.

Some analysts noted, however, that the UK still faced a few sticking points on negotiations.

"There is cautious optimism but is there going to be significant progress made by Friday, that is the real question," said Kenneth Broux, a strategist at Societe Generale.

"Clearly if there is enough progress by Friday, that will be bullish for the pound."

Bank of England Deputy Governor Dave Ramsden said on Monday he thought the floor for the central bank's key interest rate was 0.1%, but the BoE could consider going below zero to help the economy through its coronavirus crisis, lifting the pound 

"Ramsden’s comments may have prompted some GBP-traders to scale back their negative-rate bets, and that’s why the pound rallied," said a note from JFD Group.

Money market futures contracts expiring in February 2021 were back to zero after briefly pricing in negative interest rates last week.

(Reporting by Maiya Keidan; editing by Saikat Chatterjee and Ed Osmond) ((Maiya.Keidan@thomsonreuters.com; 44 207 542 1594; Reuters Messaging: maiya.keidan.thomsonreuters.com@reuters.net))