By Sam Forgione

NEW YORK (Reuters) - The British pound fell to a 31-year low against the U.S. dollar on Monday on anxiety over the aftermath of Britain's decision to quit the European Union, with analysts anticipating an even steeper drop in coming months, while the euro also dipped.

Sterling hit $1.3122 <GBP=D4>, its lowest level since mid-1985 and marking a roughly 11.7 percent fall from the currency's closing level on June 23, the day of the referendum. Analysts predicted more downside for sterling as traders monitored the fallout of the vote.

Sterling was last down 3.8 percent at $1.3182, failing to recover despite British finance minister George Osborne's assurances that the economy was in good shape and that the government and Bank of England could implement further actions.

The euro also remained weak, last down 0.9 percent at $1.1011 after hitting a session low of $1.0971. <EUR>. That session low remained slightly above Friday's 3-1/2-month low of $1.0909.

A likely fresh move for Scottish secession, and the response of the EU and its ability to contain calls by anti-EU parties across the continent, in part combined to make matters worse for sterling.

"We’re not in a full-blown panic in the pound, but the elevated level of uncertainty will leave the pound at risk of plumbing new lows," said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington.

Manimbo said reassurances from central bankers were helping to shore up sterling, but that it could still fall below $1.20 before the end of the year as an economic headwind to the UK economy sets in.

Ratings agency Standard & Poor's stripped Britain of its last remaining top-notch credit rating on Monday, but sterling remained above its session low. Analysts said traders were unsurprised by the move.

The yen edged higher against the dollar on safe-haven demand, though expectations that the Bank of Japan could intervene to halt the currency's rise limited its advance. The dollar was last down 0.3 percent against the yen, at 101.92, holding above Friday's more than 2-1/2-year low of just above 99 yen.

The dollar hit its highest level against the franc in more than three weeks, of 0.9820 franc, with analysts saying that the potential for more Swiss National Bank intervention to weaken the franc fueled the dollar's gains.

The dollar index, which measures the greenback against a basket of six major currencies, was last up 1.1 percent at 96.469 <.DXY>.

(Additional reporting by Anirban Nag in London; Editing by Nick Zieminski and Alistair Bell)