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

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

LONDON, Oct 26 (Reuters) - Cautious currency markets kept the pound subdued against a stronger dollar on Monday, but it rose slightly against the euro as an extension to Brexit talks gave markets some cause for optimism about a deal being reached before the Dec. 31 deadline.

The dollar strengthened, equities fell and markets were broadly risk-off. Analysts cited new lockdowns in Europe and record-high daily virus cases in the United States, as well as a lack of progress towards a U.S. fiscal stimulus.

The pound found some support from signs of progress in Brexit trade talks. The EU's chief negotiator, Michel Barnier, will be in London until Wednesday to try and clinch a deal, after which negotiations will switch to Brussels.

"Right now there’s a bit of optimism creeping in from the weekend developments - the extension of the talks until Wednesday," said Ned Rumpeltin, head of European currency strategy at TD Securities.

"The fact that France might be signalling some movement on fish is encouraging. We’ll see how that plays out," he said.

The pound rose in early London trading versus the dollar, then fell as the dollar strengthened. At 1606 GMT it was down 0.1% on the day at $1.3027.

Versus the euro - which is considered more indicative of market views on Brexit - the pound was up around 0.2% on the day at 90.74 pence.

Britain and the EU have just over two months left to agree on their future trading relationship, before a Dec. 31 deadline.

There are some hopes that a Brexit deal can be reached, with Ireland's Deputy Prime Minister and Northern Ireland minister Brandon Lewis expressing optimism on Sunday.

Goldman Sachs FX strategists said that Brexit developments were looking positive.

"Despite sterling's underperformance on Friday, we continue to see a path for a sharply higher GBP/USD cross into year-end," they wrote in a note.

Speculators reduced their net short position on the pound in the week to Oct. 20, for the third week running, weekly CFTC futures data showed.

TD Securities' Rumpeltin said that this could be due to a combination of market participants reining in positioning before the U.S. election and that the range of possibilities around Brexit are narrowing.

John Hardy, head of FX strategy at Saxo Bank, wrote in a note to clients that the UK's external deficit and long-term economic scarring from COVID-19 could mean that sterling does not rally as expected if a deal is reached.

"A sterling downside hedge is worth considering here if a deal arrives but fails to spark a rally," he wrote. (Reporting by Elizabeth Howcroft; editing by Emelia Sithole-Matarise, Larry King and Nick Macfie)