By Nia Williams and Dmitry Zhdannikov

CALGARY, Alberta/LONDON (Reuters) -Oil prices inched higher on Thursday, helped by late-day buying in a low-volume session to close out the week.

The market built gains overnight as Britain and the European Union reached a post-Brexit trade deal, reversed those gains, and then rebounded during the U.S. session to end modestly higher.

U.S West Texas Intermediate (WTI) crude settled up 11 cents to $48.23 a barrel, while Brent crude futures settled 9 cents higher at $51.29. Volumes were light on the last trading day before the Christmas holiday.

For the week, U.S. crude fell 1.6% while Brent lost 2%.

Markets have rallied sharply since late October as vaccines progressed to approval in numerous countries. Worldwide, infections are still growing, and investors' outlook will be clouded by the pandemic for several months.

"While the Brexit deal is supportive, the impact of COVID is the dominant driver in the oil market," said Andrew Lipow, president of Lipow Oil Associates, in Houston, Texas. "The oil market is waiting for the wider distribution of vaccines to get the public back on the road and in the air."

New strains of the coronavirus, which appear to spread the disease more quickly, have hit the United Kingdom, Nigeria, and other countries.

At least four drugmakers expect their COVID-19 vaccines will be effective against the new fast-spreading variant of the virus that is raging in Britain, and are performing tests that should provide confirmation in a few weeks.

By clinching a Brexit deal, Britain avoids a chaotic departure from one of the world's biggest trading blocs, a move many investors warned would have sparked further volatility in financial markets.

(Additional reporting by Yuka Obayashi; Editing by Richard Pullin, Mark Potter and Chizu Nomiyama)