LONDON (Reuters) - British car production fell again in August, reflecting the impact of uncertainties about Brexit on Europe's second-largest car market, an industry body said on Thursday. Overall production fell in August by an annual 5.3 percent to 103,232 units, hit by weaker demand at home and abroad, the Society of Motor Manufacturers and Traders (SMMT) said. In the first eight months of the year, output was down nearly 2 percent at 1.106 million units, mostly due to weaker sales in the British market. The drop-off follows two years of record demand. "The continuation of the longer-term downward trend in domestic demand is a concern for production across the UK," SMMT Chief Executive Mike Hawes said. "So it is vital for the future health of this sector that the current uncertainty around Brexit is removed and consumer and business confidence restored." Britain's car industry relies heavily on complex supply chains often involving other European Union countries and which could be affected by Brexit. In August, production for British customers fell by 4.4 percent as the domestic market shrank for the seventh month this year, while 5.6 percent fewer cars were made for export. The SMMT said in July its long-held target of increasing full-year production to just under 2 million units in 2020 was in doubt, in large part because of Brexit-related uncertainty. (Reporting by Polina Ivanova; Editing by William Schomberg)