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

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

LONDON, Jan 4 (Reuters) - The pound weakened against the dollar and euro on Britain's first day of trading outside the European Union on Monday, as warnings of tighter UK lockdown measures outweighed the relief over the last-minute Brexit trade deal.

Sterling initially strengthened against the dollar, even briefly breaking above $1.37 for the first time since 2018 in early London trading, but the move was more driven by dollar weakness than idiosyncratic sterling strength, with analysts still citing COVID-19 and uncertainty over the future relationship between Britain and the EU as downside risks.

At 1551 GMT on Monday, the pound was down 0.7% at $1.3573 versus the dollar, which was flat.

Against the euro, it changed hands at 90.365 pence, down around 1.1% on the day.

British Prime Minister Boris Johnson will set out further measures at 2000 GMT to try to control the rising spread in cases from the new variant of COVID-19, a spokesman said.

"When looking at GBPUSD, personally, I am not convinced that there is much more upside yet... at these levels it may be difficult to continue to push higher with further escalations in the COVID numbers and the prospect of longer, more stringent lockdowns to come," said John Goldie, FX dealer at Argentex.

"In that respect, while I do anticipate further upside for the pound this year, including a comfortable return into the 1.40s, I suspect that the virus will keep things under wraps as we start the new year," he said.

The pound had strengthened against both the dollar and euro after the Dec. 24 Brexit trade deal, which set rules for fishing, agriculture and other industries.

Although the deal does not cover Britain's finance sector, UK market participants were relieved by an extension that allows them to use platforms in the EU for swaps trading until March 2021 - a move announced on Thursday in a bid to avoid disruption.

Commerzbank's head of FX and commodity research, Ulrich Leuchtmann, said sterling's rally after the Brexit trade deal was "disappointingly limited", but that it had further scope for gains in the next few days as traders adjust their positioning upon their return from holiday.

Beyond that point, Leuchtmann was less bullish.

"For market participants with a long-term outlook the concern that Brexit might constitute the beginning of renewed economic decline in the UK is more likely to dominate," he said.

Market participants are pricing in negative rates in Britain by May 2021.

(Reporting by Elizabeth Howcroft; Editing by Hugh Lawson, Andrew Heavens and Alex Richardson)