LONDON, June 30 (Reuters) - China's yuan hit a six-month low and chalked up its biggest quarterly fall against the dollar on record on Thursday as Beijing suggested it was happy for the weakness to continue.

Chinese sources told Reuters the People's Bank of China (PBOC), China's central bank, was willing to let the yuan fall to 6.8 per dollar over the rest of the year, to support the world's No. 2 economy.

The currency, trading at 6.6 per dollar by 0950 GMT, is down roughly 3 percent since March and if falls as far as suggested, 2016 could mirror last year's record 4.5 percent drop.

"The central bank is willing to see yuan depreciation, as long as depreciation expectations are under control," a government economist, who requested anonymity, said. The central bank responded, calling the report "inaccurate".

Emerging markets (EM) were broadly higher on the day with stocks, bonds and many currencies showing a comfortable lead over developed market peers at the year's half way mark.

MSCI's main EM shares index was up 1 percent, 2.8 percent on the month and 4.5 percent for the year after some stellar performances in Latin America and Russia following an 85-percent rebound in oil prices since mid-January.

Polish and Romanian markets remained subdued in the wake of last week's Brexit vote, though mostly the concerns appeared to have largely eased.

Fund flow experts the Institute of International Finance (IIF) said the early signs showed the UK vote to quit the EU had had an no immediate impact on emerging market trading.

It said daily EM portfolio flows data suggested outflows were a fairly minor $210 million on "Brexit Friday" and that for June as a whole foreign investors had pumped a net $16.7 billion into emerging market assets.

"The markets seem to have shrugged off the Brexit concerns quite comfortably," TD Securities strategist Paul Fage said. "We have now put out recommendations to buy the currencies that have fallen but actually have very little linkage to the UK." In Asia, a widely expected move saw Taiwan trim its interest rates for the fourth consecutive meeting in a bid to shore up flagging growth. The 0.125 percentage point cut, took rates to 1.375 percent, a level last seen in mid-2010.

The Czech Republic and Romania are likely to keep their rates steady later, but Mexico could hike its rates to relieve some of the recent upward pressure on the peso.

"The consensus is for a 25 basis point hike in Mexico but we are in the minority that think they will stay on hold. We think the pressure on the peso has probably eased enough for them," Fage said.