The pound was at $1.6038 in London at 5pm, up nearly 0.2 cents on its pre-weekend close. The euro was at 84.14p in London at 5pm, down from its Friday close of 84.4p.
Sterling gained support yesterday from a speech in the US from William Dudley, president of the Federal Reserve Bank of New York, who defended the US central bank's surprise decision last week not to trim its aggressive bond-buyingscheme, which is aimed at supporting activity in the world's largest economy.
Mr Dudley said the Federal Reserve still needed to push hard against threats to the US economic recovery, and declared that fiscal uncertainties in particular "loom very large right now".
Financial markets have moved to price in a rise in UK base rates from their record low of 0.5%, at which they have stood since March 2009, in the next 18 months.
The Bank of England has signalled, based on when it expects the International Labour Organisation measure of UK unemployment to fall to 7%, that any rate rise is three years away, subject to caveats around inflation and financial stability.
Sterling hit an eight-month peak of $1.6164 on September 18, after the Fed wrongfooted financial markets by holding off from withdrawing monetary stimulus from the US economy.
The euro hit an eight-month low of 83.525p last Wednesday. Angela Merkel's victory in Sunday's German election did little to buoy the single currency.