* Chinese sources tell Reuters PBOC would accept 6.80/dollar

* Offshore yuan hits 6-month low

* Aussie falls almost one percent as major market proxy

* Sterling struggles, down more than 7 pct in June on Brexit

* Dollar slips more than 7 pct in June vs perceived safe-haven yen

By Patrick Graham

LONDON, June 30 (Reuters) - China's yuan sank to a six-month low against the dollar in offshore trade on Thursday and the Australian dollar fell almost one percent after Reuters reported the People's Bank of China is willing to let the Chinese currency weaken to 6.80 per dollar.

Government economists and advisers involved in regular policy discussions said the central bank would aim for a gradual decline for fear of triggering the sort of capital outflows that shook the economy in January and to avoid criticism from trading partners.

But they said the central bank was willing to let the currency depreciate by as much as last year's record decline of around 5 percent.

The tightly-controlled official onshore rate for the yuan, one of global investors central concerns this year, is already trading at its lowest in more than five years and is in the midst of its biggest quarterly fall ever.

"The Aussie and the yuan have just taken a big knock on that story," said Sam Lynton-Brown, a currency strategist with French bank BNP Paribas in London.

"The Aussie is now by far the biggest mover among the major currencies today as a result."

The offshore yuan fell as low as 6.70 per dollar and the Australian dollar fell as low as $0.7373.

Trade in other currencies has calmed since the shock of last week's vote by Britain to leave the European Union drove record-breaking moves in sterling and sent money flooding into the perceived security of Japan's yen and the Swiss franc.

The dollar remained near a 3-1/2-month high against a basket of currencies hit in the wake of the British vote, helped by a retreat in any expectations the U.S. Federal Reserve might have to cut interest rates this year to support growth.

Sterling was up a third of a cent against the dollar but a full cent below Wednesday's highs and the euro was down just 0.1 percent at $1.1116.

A raft of banks have forecast the pound will weaken further in the weeks ahead after sinking by as much as 18 cents against the dollar on Friday, but the currency has proved more robust since Monday. Current account data on Thursday are seen as a potential flashpoint, underlining the scale of investment Britain needs to balance its twin annual deficits.

"Today's UK current account data may get more attention than usual, given the overhang of political uncertainty and rating agency downgrades this week," RBC analysts said in a note.