* Output falls 4.0% m/m, steepest drop since April 2020

* Production of cars and car parts down 17.5%

* Economists see strong upturn if bottlenecks clear

BERLIN, Oct 7 (Reuters) - German industrial output suffered its steepest drop in August since April last year, due to supply chain disruptions that are holding back growth in Europe's biggest economy and hitting the auto sector particularly hard, official data showed on Thursday.

The Federal Statistics Office said industrial output fell by 4.0% on the month after an increase of 1.3% in July. A Reuters poll had pointed to a decline in August of 0.4%.

"Manufacturers continue to report production constraints due to supply shortages of intermediate products," the office said in a statement.

Production of cars and car parts fell by 17.5% on the month.

German car companies are struggling to meet a post-pandemic surge in demand since the start of the year, due to a lack of microchips and other intermediate products.

Carmaker BMW said its group deliveries were down 12.2% in the third quarter, hit by the microchip crunch.

On Tuesday, Daimler truck boss Martin Daum said he expected the global chip shortage to continue to affect production next year.

"We will definitely deliver less than we could have sold, and that also applies to next year," he said, adding that it was impossible to say how big the shortfalls would be.

"It's a fight for every chip," he added.

Official data released on Wednesday showed German industrial orders fell more than expected in August on weaker demand from abroad following two months of unusually strong gains due to major contracts.

However, the Munich-based Ifo economic institute said separately that its survey of production expectations rose in September.

"Order books are still full, only materials bottlenecks are causing problems at the moment and dampening production plans somewhat," Ifo economist Klaus Wohlrabe said.

Thomas Gitzel, economist at VP Bank, said "if the flow of materials gets going again, the conditions are in place for a strong upturn in industrial activity."

Carsten Brzeski, at ING, said that for now it looked like that upturn would "come rather later than sooner."

Separately, prices for newly built residential buildings rose by 12.6% on the year in August, their biggest rise since November 1970. German consumer prices rose by rose by 4.1% year-on-year last month.

Jens-Oliver Niklasch, economist at LBBW, commented: "Supply shortages, high energy prices and production stoppages: a toxic brew that already smells faintly of stagflation." (Reporting by Paul Carrel and Klaus Lauer Editing by Riham Alkousaa, Maria Sheahan and Peter Graff)