* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh

* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv

LONDON, Dec 2 (Reuters) - Sterling fell to a one-month low against the euro and also dipped momentarily below $1.33 on Wednesday as Britain and the European Union quickly approached a make-or-break moment in trade talks, with many investors doubting a deal will be reached.

Negotiators were reportedly stuck on differences over fisheries, state aid for companies and rules to resolve disputes, offsetting any optimism from Britain becoming the world's first country to approve the Pfizer-BioNTech COVID-19 vaccine.

The next 36 hours will be crucial for the British currency as investors focus on negotiations Thursday between Brexit envoys Michel Barnier and David Frost, said Jeremy Stretch, head of G10 FX strategy at CIBC Capital Markets.

Barnier told ambassadors that Brexit talks would be thrust into crisis if a UK legislation expected next week includes clauses that would breach the existing withdrawal agreement. A spokesman for Prime Minister Boris Johnson said Britain stood by the clauses in the legislation.

Ireland's foreign minister warned that if the bill deliberately breaches the Brexit divorce accord, it will be taken as a signal that London does not want a trade deal.

"We are getting very close to the end game now," Stretch said, adding that a European Council meeting on Dec. 10 in Brussels would also be seen by investors as a deadline by which to clinch a deal.

Britain left the European Union in January, with a one year transition period to negotiate a future trade deal with the bloc expiring at the end of this month.

"When you have a hard stop in terms of negotiations and you still have little movement in terms of political concessions...the risk of an unintended outcome becomes that little bit more likely," Stretch said.

European Union member states urged the bloc's chief Brexit negotiator on Wednesday not to be rushed into agreeing an unsatisfactory trade deal with Britain just because the Dec. 31 deadline is looming, a senior EU diplomat said.

Sterling last traded at $1.3329, down 0.7% on the day, after briefly falling to $1.3288 earlier, its weakest since Friday. Against the euro, it hit Oct. 27 lows of 90.83 pence . It was last down 0.8% against the common currency.

Investors' jitters were felt across derivatives markets, where costs for sterling options have increased to their highest since the beginning of November across short and medium-term maturities.

Overnight implied volatility gauges - derived from those costs - rose above 13%, the highest since Nov. 3.

Leveraged funds kept a short position in the British currency in the week to Nov. 24, according to latest Commodity Futures Trading Commission data.

The pound hit a three-month high against the dollar on Tuesday evening after UK broadcaster Times Radio said the trade deal talks had entered the "tunnel" stage of negotiations.

But the mood switched among traders as the EU's Brexit negotiator told the 27 national envoys to Brussels that differences persisted, according to a senior EU diplomat present at a closed-door briefing.

"The fact that there was a briefing completely pushed back against the view that negotiations have entered a tunnel phase," Stretch said.

That development overshadowed news that Britain had become the first western country to approve a COVID-19 vaccine, which it is likely to start rolling out next week.

(Reporting and Olga Cotaga and Thyagaraju Adinarayan; Editing by Saikat Chatterjee and John Stonestreet, Kirsten Donovan and David Gregorio)