LONDON (Reuters) - European shares fell on Monday from six-week highs as a slowdown in China’s economy stalled a global equity rally, but sterling rallied to the day’s highs after Prime Minister Theresa May promised to be more “flexible” with lawmakers over Brexit.

Trade in general was subdued with U.S. markets closed for the Martin Luther King Jr. Day but equity prices were hit after data showed the Chinese economy, the world’s second biggest, grew 6.4 percent in the fourth quarter from a year earlier, matching levels last seen in early 2009 during the global financial crisis.

The number was in line with forecasts, while factory output picked up stronger-than-expected in December and stronger services sector were some bright spots. That, along with expectations of more stimulus from Beijing, pushed Asian markets to the highest since early-December .MIAPJ0000PUS.CSI300.

But the rally in world shares appeared to end there.

A pan-European equity index .STOXX fell 1.3 percent, below six-week highs hit on Friday while Germany shares .GDAXI, heavily exposed to exports to China, was 0.6 percent lower on the day.

U.S. stock market futures, which offer an indication of how Wall Street shares will next open, were down roughly half a percent. ESc11YMc1NQc1

“It seems that the optimism we saw in Asia did not extend into Europe,” said Brittany Baumann, macro strategist at TD Securities in London.

“And the start of this week is a reflection of the downside risk that still exist - Brexit and China/U.S. trade developments.”

China’s economy faces deep and complicated changes, President Xi Jinping said on Monday.

FILE PHOTO: The German share price index DAX graph is pictured at the stock exchange in Frankfurt, Germany, January 17, 2019. REUTERS/Staff

Growing signs of weakness in China -- which has generated nearly a third of global growth in recent years -- has fueled anxiety about risks to the world economy in recent weeks and are weighing on profits for firms such as Apple. AAPL.O

“On balance, the (China) data is relatively positive and does not point to a hard landing,” said Timothy Graf, head of macro strategy at State Street Global Advisors in London.

“The consumption data being better than expected is the positive takeaway in that China is trying to engineer a move towards a consumer-led economy.”

But in other signs of caution, the Australian dollar AUD=D, often used a liquid proxy for China investments, nudged down to $0.7156.

Oil prices also fell on further evidence that economic growth in China, the world's second largest crude consumer, was easing. Brent crude oil futures LCOc1 fell 0.2 percent to $62.57 a barrel. [O/R]

BREXIT “PLAN B”

In currency markets, sterling firmed after Prime Minister Theresa May indicated she would be more “flexible” with lawmakers, even though she refused to rule out a no-deal Brexit. There are few signs she can break a deadlock with parliament after her Brexit deal was rejected last week.

May offered to tweak her defeated deal by seeking further concessions from the European Union on a backup plan to avoid a hard border in Ireland.

Sterling fell initially as she spoke, then climbed to session highs, rising above $1.29 GBP=D3. Against the euro it touched a high of 88.07 pence, up 0.2 percent on the day, reversing earlier losses.

“Her failure to detail Plan B could be the catalyst to the parliament to taking control of the process,” John Marley, a senior currency consultant at FX risk management specialist, SmartCurrencyBusiness, said.

“Ultimately that makes an extension, a deal or even a second referendum more likely.”

Britain's FTSE index .FTSE traded around flat while British government bond yields slipped 3 basis points to 1.32 percent GB10YT=RR.

For Reuters Live Markets blog on European and UK stock markets, please click on: [LIVE/]

Graphic: World FX rates in 2019 - tmsnrt.rs/2egbfVh