* Housing investment is April's only bright spot

* April factory output +6.0 pct y/y, vs f'cast +6.5 pct

* China 'is still struggling' - economist

* Jan-April fixed asset investment +10.5 pct vs f'cast +10.9 pct

* April retail sales growth +10.1 pct vs f'cast +10.5 pct (Adds analyst quote, background)

By Pete Sweeney and Jessica Macy Yu

SHANGHAI/BEIJING, May 14 (Reuters) - China's investment, factory output and retail sales all grew more slowly than expected in April, adding to doubts about whether the world's second-largest economy is stabilising.

Growth in factory output cooled to 6 percent in April, the National Bureau of Statistics (NBS) said on Saturday, disappointing analysts who expected it to rise 6.5 percent on an annual basis after an increase of 6.8 percent the prior month.

China's fixed-asset investment growth eased to 10.5 percent year-on-year in the January-April period, missing market expectations of 10.9 percent, and down from the first quarter's 10.7 percent.

Fixed investment by private firms continued to slow, indicating private businesses remain sceptical of economic prospects. Investment by private firms rose 5.2 percent year-on-year in January-April, down from 5.7 percent growth in the first quarter.

"It appears that all the engines suddenly lost momentum, and growth outlook has turned soft as well," Zhou Hao, economist at Commerzbank in Singapore, said in a research note.

"At the end of the day, we have acknowledge that China is still struggling."

Reuters reported on Saturday that China's banking regulator has sent an urgent notice to banks telling them to clear bottlenecks holding back lending to private firms.

In its data announcement, the statistics bureau said "Because the total amount of private investment is relatively large, its continued slowdown could restrain stable growth, and requires a high degree of attention."

MARCH DATA SPARKED HOPE

Retail sales growth in April, which captures both private and government purchasing, rose 10.1 percent on an annual basis, slower than expected. Analysts had forecast sales would rise 10.5 percent on an annual basis, the same percentage increase as reported for March.

It was upbeat March data that sparked hopes China's economy was picking up in a wake of a more than year-long blitz of fiscal, monetary and administrative stimulus measures. A recovering property market has also boosted demand for raw materials, giving a boost to long ailing heavy industries such as steel mills.

But much of the data on April, which included weaker-than-expected exports and imports, plus soft factory activity surveys, continued to underline lingering weakness in the broader economy.