By Gertrude Chavez-Dreyfuss

NEW YORK (Reuters) - The safe-haven yen climbed against the euro and the dollar while sterling fell to its lowest level in more than 30 years on Tuesday, as currency markets fretted about more signs of economic stress stemming from Britain's decision to leave the European Union.

The yen hit a two-week peak versus the dollar as investors went into full risk-aversion mode. So far this year, the yen has soared more than 18 percent against the greenback.

The PMI survey of purchasing managers in Britain's service sector released on Tuesday showed only a minimal fall-off in activity last month, after a disappointing reading of construction industry sentiment on Monday <ECONGB>.

The data covered the pre-Brexit period and was not all that bad. But investors took it as a negative sign as they were worried that future economic reports would show further evidence of a weakening U.K. economy, which could prompt further monetary easing from the Bank of England.

BoE Governor Mark Carney only marginally cooled expectations of further aggressive easing to combat the shock to the economy in the months ahead.

"The consequences of Brexit have put a summer U.K. interest rate cut squarely on the table, exacerbating negative sentiment toward U.K.-based assets," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington.

One important gauge of markets' appetite for risk and expectations for growth in the longer-run, U.S. 10-year Treasury yields, fell to the lowest level on record, and Carney warned that global aversion to risk might persist for some time. <US10YT=TWEB>

In the currency world, that aversion tends to drive money into traditional safe-havens such as the yen.

In late trading, the dollar fell 0.9 percent against the yen to 101.54 yen <JPY=>, after earlier declining to a two-week low of 101.46.

"We think the shrinking basket of 'safe havens' will add more downward pressure on dollar/yen and heighten the risk of unilateral intervention," wrote TD Securities in its latest research note.

The dollar dropped further after data showed new orders for U.S. factory goods fell 1.0 percent in May on weak demand for transportation and defense capital goods.

The euro dropped 1.8 percent against the yen to 112.47 yen <EURJPY=>.

Sterling was the main underperformer on Tuesday, tumbling to a 31-year low against the dollar at $1.3000 <GBP=D4>. It was last at $1.3025, down nearly 2 percent.

Against the euro, the British pound <EURGBP=D4> sank to a 2-1/2-year low, pushing the single currency to 85.48 pence. It was last up 1.3 percent at 84.98 pence.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Chizu Nomiyama and Leslie Adler)