LONDON (Reuters) - Euro zone business activity remained weak at the start of the year, a survey showed a day after the European Central Bank said the manufacturing sector remained a drag on the economy, but there were some signs the worst may be over.

IHS Markit's Euro Zone Composite Flash Purchasing Managers' Index (PMI), seen as a good gauge of economic health, held at 50.9 in January, missing the median prediction in a Reuters poll for 51.2. Anything above 50 indicates growth.

"While the year may have changed, the performance of the euro zone economy was a familiar one in January. Output growth was unchanged from the modest pace seen in December, signalling that the economy failed again to record a pick-up in growth momentum," said Andrew Harker, associate director at IHS Markit.

The headline index was bogged down by a still struggling factory industry. The manufacturing PMI marked the 12th month below the break-even mark, registering 47.8 - albeit an improvement on December's 46.3 and well above the Reuters poll's 46.8.

An index measuring output, which feeds into the composite PMI, rose to 47.5 from 46.1, its highest since August.

While most forward-looking indicators in the manufacturing PMI remained in negative territory, they were moving in the right direction. The new orders, employment, backlogs of work and quantity of purchases indexes were all still sub-50 but did rise.

However, there was evidence the bloc's dominant services industry is weakening as its PMI dropped to 52.2 from 52.8, confounding expectations for no change.

And likely of concern to policymakers, demand weakened suggesting there won't be a significant turnaround anytime soon. The services new business index fell to 51.5 from 52.1.

But optimism about the year ahead bounced. The composite future output index climbed to 61.2 from 59.4, its highest reading since September 2018.

(Reporting by Jonathan Cable; Editing by Hugh Lawson)