LONDON, Sept 23 (Reuters) - The euro and sterling slumped against the dollar on Friday after surveys showed the downturn in business activity across the euro zone and Britain deepened this month and the economies were likely entering a recession.

Also weighing on sterling, Britain's new finance minister Kwasi Kwarteng announced tax cuts and household and corporate support measures and the UK debt office laid out plans for 72 billion pounds ($79.74 billion) of additional issuance for this financial year to fund the stimulus.

Sterling was set for its biggest weekly decline against the U.S. dollar in two years after it touched a fresh 37-year low of $1.1051. At 1048 GMT it was down 1.72% at $1.1062.

British bond yields were set for their biggest daily rises in decades.

"It seems that the bounce on higher-gilt yields was little more than a short-lived sugar rush for the pound, with the reality of higher borrowing, and a larger budget deficit now starting to sink in," said Michael Brown, head of market intelligence at Caxton in London.

"The tax-cutting budget and ‘go for broke’ growth aims are unlikely to change the longer-term bearish GBP trend."

Earlier in the morning, UK PMI figures showed the downturn in Britain's economy worsened this month as companies battled soaring costs and faltering demand.

The euro slipped 0.8% to $0.9736, its lowest level since October 2002, after S&P Global's flash euro zone Composite Purchasing Managers' Index (PMI), seen as a good gauge of overall economic health, fell further in September.

The downturn in German business activity deepened, as higher energy costs hit Europe's largest economy and companies saw a drop in new business.

George Vessey, currency strategist at Western Union International Bank, said the euro zone data added pressure on the euro as it highlighted "ongoing fears about the energy crisis and recession".

Central bank policies

The yen was 0.6% lower at 142.88 per dollar, but still set for its first weekly gain in more than a month after Japanese authorities intervened in markets to support the currency for the first time since 1998.

The yen rallied more than 1% on Thursday on news that Japan had bought yen to defend the battered currency. Trading was thin on Friday with Japanese markets closed for a public holiday.

The dollar index, which measures the U.S. currency against a basket of currency including euro, sterling and yen, surged to 112.330, its highest since May 2002 and topping two-decade highs hit earlier this week. It was last up 0.8% at 112.10 and set for its best week in one month.

The Bank of England lifted interest rates by 50 basis points on Thursday in an attempt to tackle inflation but, like previous rate hikes in recent months, the move failed to support the pound as it was overshadowed by concerns about the economy.

The dollar received a boost this week from a very hawkish Federal Reserve policy announcement and rising Treasury yields.

"Ironically, I do think that the rise in U.S. Treasury yields, particularly the 10-year area, is a direct result of the view that the Bank of Japan is going to have to be selling Treasuries, to supply the dollars in order to intervene," said Ray Attrill, head of FX strategy at National Australia Bank. "Outside of dollar/yen, it will make the dollar even more attractive against other currencies."

Flash September purchasing managers' indexes for the United States were due later on Friday. ($1 = 0.9029 pounds)

(Reporting Joice Alves and Rae Wee; Editing by Susan Fenton)