BERLIN (Reuters) - German consumer prices rose slightly in June, regional data indicated on Wednesday, suggesting price pressures in Europe's largest economy are slowly picking up, but they remain weak despite the European Central Bank's ultra-loose monetary policy.

Economists have said Britain's decision to leave the European Union would further dampen growth and inflation across the euro zone, raising expectations the ECB may beef up its monetary stimulus to mitigate the impact.

The bloc has struggled with little or no inflation for the past year, caused mainly by a plunge in oil prices. The ECB expects the bloc-wide figure to stay below its target of just under 2 percent for some years.

The preliminary data from six German states, including the two most populous states of North Rhine-Westphalia and Bavaria, showed annual inflation edging up in June.

Consumer prices rose by 0.6 percent on the year in Bavaria, by 0.4 percent in North Rhine-Westphalia and by 0.4 percent in Saxony. They rose by 0.2 percent in Baden-Wuerttemberg, were unchanged in Hesse and fell by 0.1 percent in Brandenburg.

The state readings, which are not harmonized to compare with other euro zone countries, will feed into nationwide inflation data due at 1200 GMT.

Capital Economics analyst Jennifer McKeown said the state data suggested that German EU-harmonized consumer prices rose by 0.2 percent or 0.3 percent on the year.

This would be roughly in line with market expectations. The Reuters consensus forecast was a rise in annual HICP of 0.2 percent.

In May, German consumer prices rose by 0.1 percent on a non-harmonized basis and were unchanged on a harmonized basis.

For the euro zone, economists polled by Reuters expect the inflation rate, due on Thursday, to show a zero reading for June after a decline of 0.1 percent in May.

"Looking ahead, German headline inflation should continue to rise as the drag from the energy component eases," McKeown said. But she added that consumer prices were unlikely to surge.

"The pace of wage growth is still fairly subdued and will be contained by the low level of consumers' inflation expectations and uncertainty about the effects of Brexit," she noted.

The German headline inflation rate is therefore unlikely to reach two percent over the next couple of years, McKeown said, adding the ECB should increase its monetary policy support.

(Reporting by Michael Nienaber; Editing by Toby Chopra)